Sample records for nonlocal density-functional theory

We derive an exact expression for the photocurrent of photo-emission spectroscopy using time-dependent current densityfunctionaltheory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current densityfunctionaltheory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photocurrent within many-body perturbation theory. We further demonstrate that the densityfunctional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photocurrent is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.

This book deals with quantal densityfunctionaltheory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...

Partition densityfunctionaltheory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functionaltheory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based densityfunctional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.

Discusses approximation methods and applications of Quantal DensityFunctionalTheory (QDFT), a local effective-potential-energy theory of electronic structure. This book describes approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of DensityFunctionalTheory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem

We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy densityfunctional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free densityfunctionaltheory (OF-DFT) calculations.

Recently, we published an article [1] about the semiclassical origin of densityfunctionaltheory. We showed that the density and the kinetic energy density of one dimensional finite systems with hard walls can be expressed in terms of the external potential using the semiclassical Green's function method. Here, we show a uniformization scheme for the semiclassical density and the kinetic energy density for turning-point problems.[1] P. Elliott, D. Lee, A. Cangi, and K. Burke, Phys. Rev. Lett. 100, 256406 (2008).

In this article techniques for including dispersion interactions within densityfunctionaltheory are examined. In particular comparisons are made between four popular methods: dispersion corrected DFT, pseudopotential correction schemes, symmetry adapted perturbation theory, and a non-localdensityfunctional - the so called Rutgers-Chalmers van der Waals densityfunctional (vdW-DF). The S22 benchmark data set is used to evaluate the relative accuracy of these methods and factors such as scalability and transferability are also discussed. We demonstrate that vdW-DF presents an excellent compromise between computational speed and accuracy and lends most easily to full scale application in solid materials. This claim is supported through a brief discussion of a recent large scale application to H2 in a prototype metal organic framework material (MOF), Zn2BDC2TED. The vdW-DF shows overwhelming promise for first-principles studies of physisorbed molecules in porous extended systems; thereby having broad applicability for studies as diverse as molecular adsorption and storage, battery technology, catalysis and gas separations.

We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the densityfunctionaltheory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.

Complexes with pincer ligand moieties have garnered much attention in the past few decades. They have been shown to be highly active catalysts in several known transition metal-catalyzed organic reactions as well as some unprecedented organic transformations. At the same time, the use of computational organometallic chemistry to aid in the understanding of the mechanisms in organometallic catalysis for the development of improved catalysts is on the rise. While it was common in earlier studies to reduce computational cost by truncating donor group substituents on complexes such as tertbutyl or isopropyl groups to hydrogen or methyl groups, recent advancements in the processing capabilities of computer clusters and codes have streamlined the time required for calculations. As the full modeling of complexes become increasingly popular, a commonly overlooked aspect, especially in the case of complexes bearing isopropyl substituents, is the conformational analysis of complexes. Isopropyl groups generate a different conformer with each 120 ° rotation (rotamer), and it has been found that each rotamer typically resides in its own potential energy well in densityfunctionaltheory studies. As a result, it can be challenging to select the most appropriate structure for a theoretical study, as the adjustment of isopropyl substituents from a higher-energy rotamer to the lowest-energy rotamer usually does not occur during structure optimization. In this report, the influence of the arrangement of isopropyl substituents in pincer complexes on calculated complex structure energies as well as a case study on the mechanism of the isomerization of an iPrPCP-Fe complex is covered. It was found that as many as 324 rotamers can be generated for a single complex, as in the case of an iPrPCP-Ni formato complex, with the energy difference between the global minimum and the highest local minimum being as large as 16.5 kcalmol-1. In the isomerization of a iPrPCP-Fe complex, it was found

A fully non-local exchange-correlation formalism within the framework of densityfunctionaltheory, known as the weighted density approximation (WDA), has been applied to the conjugated polymer poly-para-phenylene vinylene (PPV) and is shown to lead to a marked improvement in the agreement of theory and experiment for the electronic band structure of the conjugated polymer. In particular, some new model WDA functions are developed, which substantially increase the electronic band gap of the polymer relative to those obtained with the local density approximation and generalized gradient approximation. The calculated band gap of PPV is quantitatively or at 1east semiquantitatively in agreement with the experimental data.

We propose a multiconfigurational hybrid density-functionaltheory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

We propose a multiconfigurational hybrid density-functionaltheory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

This book examines densityfunctionaltheory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.

We present a new theoretical framework, called Multiconfiguration Pair-DensityFunctionalTheory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of densityfunctionaltheory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of densityfunctionals by translating conventional densityfunctionals of the spin densities using a simple prescription, and we perform post-SCF densityfunctional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of densityfunctionals, that is comparable to much more expensive multireference perturbation theory methods.

We propose a multiconfigurational hybrid density-functionaltheory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension of the usual hybrid approximations by essentially adding a fraction \\lambda of exact static correlation in addition to the fraction \\lambda of exact exchange. Test calculations on the cycloaddition reactions of ozone with ethylene or acetylene and the dissociation of diatomic molecules with the Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) densityfunctionals show that a good value of \\lambda is 0.25, as in the usual hybrid approximations. The results suggest that the proposed multiconfigurational hybrid approximations can improve over usual density-functional calculations for situations with strong static correlation effects.

Non-covalent interactions are essential in the description of soft matter, including materials of technological importance and biological molecules. In density-functionaltheory, common approaches fail to describe dispersion forces, an essential component in noncovalent binding interactions. In the last decade, great progress has been made in the development of accurate and computationally-efficient methods to describe noncovalently bound systems within the framework of density-functionaltheory. In this review, we give an account of the field from a chemical and didactic perspective, describing different approaches to the calculation of dispersion energies and comparing their accuracy, complexity, popularity, and general availability. This review should be useful to the newcomer who wants to learn more about noncovalent interactions and the different methods available at present to describe them using density-functionaltheory.

Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...

Semilocal densityfunctionaltheory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal densityfunctionaltheory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.

The adiabatic connection formula of ground-state densityfunctionaltheory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal densityfunctionaltheory is cast as an integral over temperatures instead, ranging upwards from the system's physical temperature to infinite temperatures. Several formulas yield one component of the thermal correlation free energy in terms of another, many of which can be expressed either in terms of temperature- or coupling-constant integration. We illustrate with the uniform electron gas.

Degenerate perturbation theory from quantum mechanics is inadequate in densityfunctionaltheory (DFT) because of nonlinearity in the Kohn-Sham potential. We develop the fully general degenerate perturbation theory for DFT without assuming that the degeneracy is required by symmetry. The resulting methodology is applied to the iron atom ground state in order to demonstrate the effects of degeneracy that appears both due to symmetry requirements and accidentally, between different representations of the symmetry group.

Densityfunctionaltheory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.

Today, quantum mechanical densityfunctionaltheory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of densityfunctionaltheory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school.

This book is on quantal densityfunctionaltheory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn densityfunctionaltheory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical densityfunctionaltheory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field densityfunctionaltheory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local densityfunctionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

Demonstrates how anyone in math, science, and engineering can master DFT calculations Densityfunctionaltheory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. DensityFunctionalTheory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...

Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of densityfunctionaltheory calculations using 6-311++ g (d, p) basis set and B3LYP functional.

Densityfunctional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any densityfunctional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.

Densityfunctionaltheory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties. The errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These errors can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently.

We introduce a nonequilibrium density-functionaltheory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the energy-density operator. We identify the excess-energy density, in addition to the particle density, as the basic variable, which is reproduced by an effective noninteracting Kohn-Sham system. A novel Kohn-Sham equation emerges featuring a time-dependent and spatially varying mass which represents local temperature variations. The adiabatic contribution to the Kohn-Sham potentials is related to the entropy viewed as a functional of the particle and energy density. Dissipation can be taken into account by employing linear response theory and the thermoelectric transport coefficients of the electron gas.

Degenerate perturbation theory from quantum mechanics is inadequate in densityfunctionaltheory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3 d orbitals, as well as accidental degeneracy, between the 3 d and 4 s orbitals. The quadrupole potential couples the degenerate 3 d and 4 s states, serving as an example of the most general perturbation.

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. While density-functionaltheory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchange-correlation energy functional and lead to different exact conditions on this functional. Finally, we suggest some possible directions for future developments.

We propose a nonlocaldensityfunctionaltheory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.

Three dimensional implementations of liquid state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular densityfunctionaltheory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short range. The approach is shown to provide the correct three-dimensional microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two-three orders of magnitude lower tha...

First-principles calculations based on densityfunctionaltheory have been widely used in studies of the structural, thermoelastic, rheological, and electronic properties of earth-forming materials. The exchange-correlation term, however, is implemented based on various approximations, and this is believed to be the main reason for discrepancies between experiments and theoretical predictions. In this work, by using periclase MgO as a prototype system we examine the discrepancies in pressure and Kohn-Sham energy that are due to the choice of the exchange-correlation functional. For instance, we choose local density approximation and generalized gradient approximation. We perform extensive first-principles calculations at various temperatures and volumes and find that the exchange-correlation-based discrepancies in Kohn-Sham energy and pressure should be independent of temperature. This implies that the physical quantities, such as the equation of states, heat capacity, and the Gr\\"{u}neisen parameter, estimat...

The thermodynamical properties of the main phases of metallic polonium are examined using densityfunctionaltheory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.

DensityFunctionalTheory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contain...

The treatment of adiabatic perturbations within density-functionaltheory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.

Forty-five years after the point de d\\'epart [1] of densityfunctionaltheory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the "divine" energy functional in terms of the electron density [2] still eludes us --and possibly will do so forever [3]. In what follows we examine a formulation in the same spirit with phase-space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the T...

One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids. In the intermediate mesoscopic length scale, an appropriate picture of the equilibrium and dynamical processes has been obtained through the single particle number density of the constituent atoms or molecules. A wide class of problems involving nanomaterials, interfacial science and soft condensed matter has been addressed using the density based theoretical formalism as well as atomistic simulation in this regime. In the macroscopic length scale, however, matter is usually treated as a continuous medium and a description using local mass density, energy density and other related densityfunctions has been found to be quite appropriate. A unique single unified theoretical framework that emerges through the density concept at these diverse length scales and is applicable to both quantum and classical systems is the so called densityfunctionaltheory (DFT) which essentially provides a vehicle to project the many-particle picture to a single particle one. Thus, the central equation for quantum DFT is a one-particle Schrödinger-like Kohn–Sham equation, while the same for classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential. Selected illustrative applications of quantum DFT to microscopic modeling of intermolecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are presented.

Multicomponent densityfunctionaltheory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF(-) molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

Multicomponent densityfunctionaltheory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF- molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) densityfunctionaltheory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-densityfunctionaltheory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of densityfunctional called an on-top densityfunctional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top densityfunctionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of densityfunctionaltheory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

In this work we demonstrate that densityfunctionaltheory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.

Densityfunctionaltheory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.

The time evolution of a system consisting of electrons and ions is often treated in the Born-Oppenheimer approximation, with electrons in their instantaneous ground state. This approach cannot capture many interesting processes that involved excitation of electrons and its effects on the coupled electron-ion dynamics. The time scale needed to accurately resolve the evolution of electron dynamics is atto-seconds. This poses a challenge to the simulation of important chemical processes that typically take place on time scales of pico-seconds and beyond, such as reactions at surfaces and charge transport in macromolecules. We will present a methodology based on time-dependent densityfunctionaltheory for electrons, and classical (Ehrenfest) dynamics for the ions, that successfully captures such processes. We will give a review of key features of the method and several applications. These illustrate how the atomic and electronic structure evolution unravels the elementary steps that constitute a chemical reaction. In collaboration with: G. Kolesov, D. Vinichenko, G. Tritsaris, C.M. Friend, Departments of Physics and of Chemistry and Chemical Biology.

Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is densityfunctionaltheory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature densityfunctionaltheory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the

The universality principle of the free energy densityfunctional and the ‘test particle' trick by Percus are combined to construct the approximate free energy densityfunctional or its functional derivative. Information about the bulk fluid ralial distribution function is integrated into the densityfunctional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum densityfunctionaltheory.

The Hohenberg-Kohn densityfunctional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to densityfunctional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of densityfunctional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate densityfunctionals are discussed.

We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.

The nonlocal van der Waals densityfunctional (vdW-DF) captures the essential physics of the dispersion interaction not only in the asymptotic regime but also for a general case of overlapping fragment densities. A balanced treatment of other energetic contributions, such as exchange, is crucial if we aim for accurate description of various properties of weakly bound systems. In this paper, the vdW-DF correlation functional is modified to make it better compatible with accurate exchange functionals. We suggest a slightly simplified construction of the nonlocal correlation, yielding more accurate asymptotic C(6) coefficients. We also derive a gradient correction, containing a parameter that can be adjusted to suit an exchange functional of choice. We devise a particularly apt combination of exchange and correlation terms, which satisfies many important constraints and performs well for our benchmark tests.

We investigate the nonlocal gravity theory by deriving nonlocal equations of motion using the traditional variation principle in a homogeneous background. We focus on a class of models with a linear nonlocal modification term in the action. It is found that the resulting equations of motion contain the advanced Green's function, implying that there is an acausality problem. As a consequence, a divergence arises in the solutions due to contributions from the future infinity unless the Universe will go back to the radiation dominated era or become the Minkowski spacetime in the future. We also discuss the relation between the original nonlocal equations and its biscalar-tensor representation and identify the auxiliary fields with the corresponding original nonlocal terms. Finally, we show that the acusality problem cannot be avoided by any function of nonlocal terms in the action.

We propose an in silico experiment to introduce the classical densityfunctionaltheory (cDFT). Densityfunctionaltheories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…

We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave-function correlated and densityfunctionaltheory methods. We found that second-order correlation methods describe relatively well the dihydrogen complexes. However, for high accuracy inclusion of triple contributions is important. On the other hand, none of the considered densityfunctional methods can simultaneously yield accurate bond lengths and interaction energies. However, we found that improved results can be obtained by the inclusion of non-local exchange contributions.

We construct a nonlocaldensityfunctional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent densityfunctional with full exact exchange. It satisfies other known

A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using densityfunctionaltheory. Achievements were: (1) First densityfunctionaltheory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.

Aspects of densityfunctional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state densityfunctionaltheory (DFT), are studied in detail. The asymptotic behavior of the complex densityfunction is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.

Reparametrization of Wigner's correlation energy densityfunctional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the densityfunctional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).

Range-separated hybrid methods between wave function theory and densityfunctionaltheory (DFT) can provide high-accuracy results, while correcting some of the inherent flaws of both the underlying wave function theory and DFT. We here assess the accuracy for excitation energies of the nucleobases...

Within the nuclear densityfunctionaltheory (DFT) we study the effect of reflection-asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver AxialHFB that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy densityfunctionals. Illustrative calculations are carried out for even-even isotopes of radium and thorium.

We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller densityfunctionaltheory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller densityfunctional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures.

We present here an introductory practical course to classical densityfunctionaltheory (cDFT). Densityfunctionaltheories, whether quantum or classical, rely largely on nonintuitive abstract concepts and applied mathematics. They are nevertheless a powerful tool and an active field of research in physics and chemistry that led to the 1998 Nobel prize in chemistry. We here illustrate the DFT in its most mathematically simple and yet physically relevant form: the classical densityfunctionaltheory of an ideal fluid in an external field, as applied to the prediction of the structure of liquid neon at the molecular scale. This introductory course is built around the production of a cDFT code written by students using the Mathematica language. In this way, they are brought to deal with (i) the cDFT theory itself, (ii) some basic concepts around the statistical mechanics of simple fluids, (iii) the underlying mathematical and numerical problem of functional minimization, and (iv) a functional programming languag...

We derive the basic formalism of densityfunctionaltheory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried ou

Range-separated density-functionaltheory is an alternative approach to Kohn-Sham density-functionaltheory. The strategy of range-separated density-functionaltheory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functionaltheory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whe...

The scope of time-dependent density-functionaltheory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...

Range-separated density-functionaltheory (DFT) is an alternative approach to Kohn-Sham density-functionaltheory. The strategy of range-separated density-functionaltheory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functionaltheory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functionaltheory based on an exponential formula.

We propose densityfunctionaltheory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows densityfunctionaltheory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

We develop a stochastic formulation of the optimally-tuned range-separated hybrid densityfunctionaltheory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham densityfunctionaltheory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advan...

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent densityfunctionaltheory. Effective permittivity and permeability coefficients are obtained.

amount of experimental data gathered during the last decades. This article shows how densityfunctionaltheory can be used to describe the state of the surface during reactions and the rate of catalytic reactions. It will also show how we are beginning to understand the variation in catalytic activity...

We introduce a conceptual framework which allow us to treat charge and spin fluctuations about the Local density Approximation (LDA) to the DensityFunctionalTheory (DFT). We illustrate the approach by explicit study of the Disordered Local Moment (DLM) state in Fe above the Curie Temperature {Tc} and the Mott insulating state in MnO. 27 refs., 6 figs.

We give here an overview of the orbital-free densityfunctionaltheory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

Walter Kohn transformed theoretical chemistry and solid statephysics with his development of densityfunctionaltheory, forwhich he was awarded the Nobel Prize. This article tries toexplain, in simple terms, why this was an important advancein the field, and to describe precisely what it was that he (togetherwith his collaborators Pierre Hohenberg and Lu JeuSham) achieved.

We construct exact Kohn-Sham potentials for the ensemble density-functionaltheory (EDFT) of excited states from the ground and excited states of helium. The exchange-correlation potential is compared with current approximations, which miss prominent features. The ensemble derivative discontinuity is tested, and the virial theorem is proven and illustrated.

The widespread popularity of densityfunctionaltheory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We r...

The van Leeuwen proof of linear-response time-dependent densityfunctionaltheory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation (XC) approximations.

A theory is developed for magnetically confined Fermi gas at a low temperature based on the densityfunctionaltheory. The theory is illustrated by the numerical calculation of the density distributions of Fermi atoms 40K with parameters according to DeMarco and Jin's experiment [Science, 285(1999)1703]. Our results are in close agreement with the experiment. To check the theory, we also performed calculations using our theory at a high temperature, which compared very well to the results of the classical limit.

A consistent combination of covariant densityfunctionaltheory (CDFT) and Landau-Migdal Theory of Finite Fermi Systems (TFFS) is presented. Both methods are in principle exact, but Landau-Migdal theory cannot describe ground state properties and densityfunctionaltheory does not take into account the energy dependence of the self-energy and therefore fails to yield proper single-% particle spectra as well as the coupling to complex configurations in the width of giant resonances. Starting from an energy functional, phonons and their vertices are calculated without any further parameters. They form the basis of particle-vibrational coupling leading to an energy dependence of the self-energy and an induced energy-dependent interaction in the response equation. A subtraction procedure avoids double counting. Applications in doubly magic nuclei and in a chain of superfluid nuclei show excellent agreement with experimental data.

We explore the local and nonlocal response functions of the grand canonical potential densityfunctional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the densityfunctionaltheory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.

We explore the local and nonlocal response functions of the grand canonical potential densityfunctional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the densityfunctionaltheory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.

In this thesis, applications and development will be presented within the field of van der Waals interactions in densityfunctionaltheory. The thesis is based on the three projects: i) van der Waals interactions effect on the structure of liquid water at ambient conditions, ii) development...... and benchmarking of a new van der Waals densityfunctional, and iii) the application of the newly developed functional to CO desorption from Ru(0001). The effect of van der Waals interactions in water was studied by performing ab initio molecular dynamics simulations using PBE and the two recent van der Waals...... densityfunctionals optPBE-vdW and vdW-DF2 with identical computational setup. The two van der Waals functionals have been found to give excellent descriptions of the constituents of water (e.g., water dimers and hexamers). Including van der Waals interactions gives a softer water structure as seen from...

Structural phase transitions caused by high pressure or temperature are very relevant in materials science. The high pressure transitions are essential to understand the interior of planets. Pressure or temperature induced phase transitions can be relevant to understand other phase transitions in strongly correlated systems or molecular crystals.Phase transitions are important also from the aspect of method development. Lower level densityfunctionals, LSDA and GGAs all fail to predict the lattice parameters of different polymorphs and the phase transition parameters at the same time. At this time only nonlocaldensityfunctionals like HSE and RPA have been proved to resolve the geometry-energy dilemma to some extent in structural phase transitions. In this talk I will report new results from the MGGA_MS family of meta-GGAs and give an insight why this type of meta-GGAs can give a systematic improvement of the geometry and phase transition parameters together. I will also present results from the RPA and show a possible way to improve beyond RPA.

In the thirty-two years since the birth of the foundational theorems, time-dependent densityfunctionaltheory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.

Multistate densityfunctionaltheory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn-Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained densityfunctionaltheory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor-acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer.

Modern densityfunctionaltheory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic densityfunctionaltheory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.

The main goal of the present contribution is a pedagogical introduction to the fascinating world of neutron stars by relying on relativistic densityfunctionaltheory. Densityfunctionaltheory provides a powerful--and perhaps unique--framework for the calculation of both the properties of finite nuclei and neutron stars. Given the enormous densities that may be reached in the core of neutron stars, it is essential that such theoretical framework incorporates from the outset the basic principles of Lorentz covariance and special relativity. After a brief historical perspective, we present the necessary details required to compute the equation of state of dense, neutron-rich matter. As the equation of state is all that is needed to compute the structure of neutron stars, we discuss how nuclear physics--particularly certain kind of laboratory experiments--can provide significant constrains on the behavior of neutron-rich matter.

A spin projected double-hybrid densityfunctionaltheory is presented that accounts for different scaling of opposite and same spin terms in the second order correction. This method is applied to three dissociation reactions which in the unprojected formalism exhibit significant spin contamination with higher spin states. This gives rise to a distorted potential surface and can lead to poor geometries and energies. The projected method presented is shown to improve the description of the potential over unprojected double hybrid densityfunctionaltheory. Comparison is made with the reference states of the two double hybrid functionals considered here (B2PLYP and mPW2PLYP) in which the projected potential surface is degraded by an imbalance in the description of dynamic and static correlation.

Densityfunctional calculations for the electronic conductance of single molecules attached to leads are now common. I'll examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. Finally, I will compare and contrast several new methodologies that go beyond the present standard approach of applying the Landauer formula to ground-state DFT. Self-interaction errors in densityfunctional calculations of electronictransport, C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005) The Dramatic Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations, S-H. Ke, H.U. Baranger, and W. Yang, cond-mat/0609367. Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula, M. Koentopp, K. Burke, and F. Evers, Phys. Rev. B Rapid Comm., 73, 121403 (2006). DensityFunctionalTheory of the Electrical Conductivity of Molecular Devices, K. Burke, Roberto Car, and Ralph Gebauer, Phys. Rev. Lett. 94, 146803 (2005). Densityfunctional calculations of nanoscale conductance, Connie Chang, Max Koentopp, Kieron Burke, and Roberto Car, in prep.

The past decades have seen densityfunctionaltheory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.

This is the author accepted manuscript.The final version is available from the American Association for the Advancement of Science via http://dx.doi.org/10.1126/science.aad3000 The widespread popularity of density-functionaltheory has given rise to a vast range of dedicated codes to predict molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions on the reproducibility of such predictions. We report the results of a community-...

Periodic DensityFunctionalTheory calculations are capable of providing powerful insights into the structural, energetics, and electronic phenomena that underlie heterogeneous catalysis on transition metal nanoparticles. Such calculations are now routinely applied to single crystal metal surfaces...... and to subnanometer metal clusters. Descriptions of catalysis on truly nanosized structures, however, are generally not as well developed. In this talk, I will illustrate different approaches to analyzing nanocatalytic phenomena with DFT calculations. I will describe case studies from heterogeneous catalysis...

When developing and assessing densityfunctionaltheory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In addition, the dependency of the semiempirical fits to a given basis set for a generalised gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability.

Fractional occupation numbers can produce open-shell degeneracy in densityfunctionaltheory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate state connects to a single perturbed state which extremizes, but does not necessarily minimize or maximize, the energy with respect to occupation numbers. Using a system of three electrons in a harmonic oscillator potential, we relate the counterintuitive sign of first-order occupation numbers to eigenvalues of the electron-electron interaction Hessian.

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy densityfunctionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with densityfunctionaltheory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonst...

Full Text Available Abstract: We discuss the basic concepts of densityfunctionaltheory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy densityfunctional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.

Nuclear densityfunctionaltheory (DFT) is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy densityfunctional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we use the concept of nucleonic localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.

theory for water which overcomes this difficulty and gives reasonable agreement with molecular dynamics simulation data for the solvation of hard spheres in water and sufficient agreement with experimental data for hydration of inert gas atoms to justify its use in a joint theory with standard approximate densityfunctionals used in electronic structure calculations. The last study in the thesis combines the previous ideas and presenting an approximate model densityfunctional which includes a description of cavitation effects through a classical density-functionaltheory; a description of dielectric effects through a non-local polarizability, and a description of the coupling of the solvent to the electrons of the solute through a pseudopotential. Without any empirical fitting of parameters to solvation data, this theory predicts solvation energies at least as well as state-of-the-art quantum-chemical cavity approaches, which do employ such fitting. Although this agreement without adjustable parameters is very encouraging and shows the promise of the joint density-functional approach, the functionals which we develop here are models and do not yet include all of the microscopic physics. The thesis concludes with a description of the directions future work should take to address this weakness.

The universal densityfunctional F of density-functionaltheory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functionaltheory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.

The universal densityfunctional F of density-functionaltheory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functionaltheory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.

The accuracy of densityfunctionaltheory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.

We present a practical scheme for performing error estimates for density-functionaltheory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...... for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude...

We apply standard densityfunctionaltheory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially...... and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides...

We present a force field for bulk alumina (Al2O3), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with densityfunctionaltheory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.

The structural and electronic properties of rutile and anatase, and the influence of both mono- and co-doping, have been studied using DensityFunctionalTheory. Ge-doped anatase and rutile exhibit different band gap-narrowing mechanisms; in particular, host Ti 3d states move to lower energy regions in anatase and Ge 4s impurities states locate below the conduction band of rutile. For S-doping, S 3p states locate above the top of the valence band and mix with O 2p states, leading to band gap ...

Time-dependent density-functionaltheory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s

INTRODUCTION: The cytochrome P450 enzymes (CYPs) metabolize many drug compounds. They catalyze a wide variety of reactions, and potentially, a large number of different metabolites can be generated. Densityfunctionaltheory (DFT) has, over the past decade, been shown to be a powerful tool...... isoforms. This is probably due to the fact that the binding of the substrates is not the major determinant. When binding of the substrate plays a significant role, the well-known issue of determining the free energy of binding is the challenge. How approaches taking the protein environment into account...

We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical densityfunctionaltheory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear DensityFunctionalTheory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.

We have performed densityfunctionaltheory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.

Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear densityfunctionaltheory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different densityfunctionaltheory methods, namely an ultrasoft pseudopotential plane-wave code...... in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k(parallel to) points in the surface plane. For all systems we find...

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic DensityFunctionalTheory (DDFT) [M. Rex and H. Löwen, “Dynamical densityfunctionaltheory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-densityfunctionaltheory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within densityfunctionaltheory.

Static and dynamical densityfunctional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current DensityFunctionaltheory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.

Full Text Available The scope of time-dependent density-functionaltheory (TDDFT is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most. In the static regime, density-functional perturbation theory (DFPT allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix element of the resolvent of the Kohn-Sham Liouvillian super-operator. A DFPT representation of response functions allows one to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is finally conveniently evaluated using a newly developed non-symmetric Lanczos technique, which allows for the calculation of the entire spectrum with a single Lanczos recursion chain. Each step of the chain essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian or, for that matter, as a single time step of a Car-Parrinello molecular dynamics run. The method will be illustrated with a few case molecular applications.

A systematic investigation of even-even superheavy elements in the region of proton numbers $100 \\leq Z \\leq 130$ and in the region of neutron numbers from the proton-drip line up to neutron number $N=196$ is presented. For this study we use five most up-to-date covariant energy densityfunctionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range and deformation effects are taken into account. This allows us to assess the spread of theoretical predictions within the present covariant models for the binding energies, deformation parameters, shell structures and $\\alpha$-decay half-lives. Contrary to the previous studies in covariant densityfunctionaltheory, it was found that the impact of $N=172$ spherical shell gap on the structure of superheavy elemen...

Time-dependent densityfunctionaltheory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole...... moments are computed using the same geometries (MP2/6-31G*) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio...

In the framework of densityfunctionaltheory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.

Within the energy densityfunctional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.

Nuclear densityfunctionaltheory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.

Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent densityfunctionaltheory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.

A classical densityfunctionaltheory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation functions. Those functions can be computed by using molecular simulations such as molecular dynamic or Monte Carlo. It is also possible to use functions that have been determined experimentally. The functional minimization gives access to the solvation free energy and to the equilibrium solvent density. Some correction to the functional are also proposed to get the proper tetrahedral order of solvent molecules around a charged solute and to reproduce the correct long range hydrophobic behavior of big apolar solutes. To proceed the numerical minimization of the functional, the theory has been discretized on two tridimensional grids, one for the space coordinates, the other for the angular coordinates, in a functional minimization code written in modern Fortran, mdft. This program i...

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy densityfunctionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with densityfunctionaltheory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.

The universal densityfunctional $F$ of density-functionaltheory is a complicated and ill-behaved function of the density--in particular, $F$ is not differentiable, making many formal manipulations more complicated. Whilst $F$ has been well characterized in terms of convex analysis as forming a conjugate pair $(F,E)$ with the ground-state energy $E$ via the Hohenberg-Kohn and Lieb variation principles, $F$ is only subdifferentiable on a small (but dense) set of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any $\\epsilon>0$, pairs of conjugate functionals $({}^\\epsilon\\!E,{}^\\epsilon\\! F)$ that converge to $(E,F)$ pointwise everywhere as $\\epsilon\\rightarrow 0^+$, and such that ${}^\\epsilon\\!F$ is (Fr\\'echet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box, which does not change the physics. It is noteworthy that no information is lost in the Moreau-Yosida regularization...

We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasi-local (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasi-local kernels all acausal effects are confined within the compact support regi...

The formalism developed in the first paper of the series [arXiv:0901.1060v3] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-densityfunctionaltheory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determina...

The Fermi surface is an abstract object in the reciprocal space of a crystal lattice, enclosing the set of all those electronic band states that are filled according to the Pauli principle. Its topology is dictated by the underlying lattice structure and its volume is the carrier density in the material. The Fermi surface is central to predictions of thermal, electrical, magnetic, optical and superconducting properties in metallic systems. Densityfunctionaltheory is a first-principles method used to estimate the occupied-band energies and, in particular, the isoenergetic Fermi surface. In this review we survey several key facts about Fermi surfaces in complex systems, where a proper theoretical understanding is still lacking. We address some critical difficulties.

Full Text Available Using hybrid densityfunctionaltheory and a relatively large basis set, the lowest energy equilibrium structure, vibrational spectrum, and natural orbital analysis were obtained for magnesium diboride clusters [(MgB2x for x=1,2, and 3]. For comparison, boron clusters [BxÃ‚Â forÃ‚Â x=2,4,Ã‚Â andÃ‚Â 6] were also considered. The MgB2 and (MgB22 showed equilibrium structures with the boron atoms in arrangements similar to what was obtained for pure boron atoms, whereas, for (MgB23 a different arrangement of boron was obtained. From the population analysis, large electron density in the boron atoms forming the clusters was observed.

The exothermic reaction of HCS with OH on the single-state potential energy surface was explored by means of DensityFunctionTheory(DFT). The equilibrium structural parameters, the harmonic vibrational frequencies, the total energies and the zero point energies(ZPE) of all the species in the reaction were computed. Six intermediates and seven transition states were located, three exothermic channels were found. The frequency analysis and the Intrinsic Reaction Coordinate(IRC) calculation confirm that the transitions are truthful. The results indicate that there are three exothermic channels and their corresponding products are: P1(H2O+CS), P2(H2S+CO), P3(OCS+H2), and P1 has a larger branch ratio.

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two electron systems, exploring the behavior of exact ensemble densityfunctionaltheory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for both exchange and correlation, and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble densityfunctionaltheory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.

The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, densityfunctionaltheory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.

The single-impurity Anderson model is studied within the i-DFT framework, a recently proposed extension of densityfunctionaltheory (DFT) for the description of electron transport in the steady state. i-DFT is designed to give both the steady current and density at the impurity, and it requires the knowledge of the exchange-correlation (xc) bias and on-site potential (gate). In this work we construct an approximation for both quantities which is accurate in a wide range of temperatures, gates, and biases, thus providing a simple and unifying framework to calculate the differential conductance at negligible computational cost in different regimes. Our results mark a substantial advance for DFT and may inform the construction of functionals applicable to other correlated systems.

Full Text Available Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic DensityFunctionalTheory (DDFT extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth.

@@ A non-mean field densityfunctionaltheory is employed to investigate the vapour-liquid nucleation. The excess Helmholtz free energy functional is formulated in terms of a local density approximation for short ranged repulsion and a density-gradient expansion for long-ranged attractions. An analytical expression for the direct correlation function of a Lennard-Jones fluid is utilized to take into account the effect of long-ranged attractions on intermolecular correlations. With the predicted bulk properties and surface tension as input, the nucleation properties including density profile, work of formation and number of particles at the reduced temperatures T* = 0.694 and 0.741 are inuestigated. The obtained number of particles in the critical nucleus agrees well with the simulation data.

Pyrite (FeS2) bulk and (100) surface properties and the oxygen adsorption on the surface were studied by using densityfunctionaltheory methods. The results show that in the formation of FeS2 (100) surface, there exists a process of electron transfer from Fe dangling bond to S dangling bond. In this situation, surface Fe and S atoms have more ionic properties. Both Fe2+ and S2- have high electrochemistry reduction activity, which is the base for oxygen adsorption. From the viewpoint of adsorption energy, the parallel form oxygen adsorption is in preference.The result also shows that the state of oxygen absorbed on FeS2 surface acts as peroxides rather than O2.

A number of densityfunctionaltheory (DFT) methods were used to calculate the electrostatic potential for the series of molecules N2, F2, NH3, H2O, CHF3, CHCl3, C6H6, TiF4, CO(NH2)2 and C4H5N3O compared with QCISD (quadratic configuration interaction method including single and double substitutions) results. Comparisons were made between the DFT computed results and the QCISD ab initio ones and MP2 ab initio ones, compared with the root-mean-square deviation and electrostatic potential difference contours figures. It was found that the hybrid DFT method B3LYP, yields electrostatic potential in good agreement with the QCISD results. It is suggest this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.

A class of metal disilicides (of the form XSi2, where X is a divalent metal) crystallizes in the EuGe2 structure, formed by hexagonal corrugated silicon planes intercalated with metal atoms. These compounds are superconducting like other layered superconductors, such as MgB2. Moreover, their properties can be easily tuned either by external pressure or by negative chemical pressure (i.e., by changing the metal), which makes disilicides an ideal testbed to study superconductivity in layered systems. In view of this, we present an extensive densityfunctionaltheory study of the electronic and phonon band structures as well as the electron-phonon interaction of metal disilicides. Our results explain the variation of the superconducting transition temperature with pressure and the species of the intercalating atom, and allow us to predict superconductivity for compounds not yet synthesized belonging to this family.

Inspired by an effective field theory (EFT) for Fermi systems, we write the nuclear energy densityfunctional (EDF) as an expansion in powers of the Fermi momentum $k_F$, or the cubic root of the density $\\rho^{1/3}$. With the help of pseudodata from microscopic calculations we fit the coefficients of the functional within a wide range of densities relevant for nuclei and neutron stars. The functional already at low order can reproduce known or adopted values of nuclear matter near saturation, a range of existing microscopic results on asymmetric matter, and a neutron-star mass-radius relation consistent with observations. Our approach leads to a transparent expansion of Skyrme-type EDFs and opens up many possibilities for future explorations in nuclei and homogeneous matter.

Large scale DensityFunctionalTheory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471

An overview of recent developments and applications of a specific densityfunctional approach that originates from Rosenfeld's fundamental measure theory for hard spheres is given. Model systems that were treated include penetrable spheres that interact with a step function pair potential, the Widom-Rowlinson model, the Asakura-Oosawa colloid-polymer mixture, ternary mixtures of spheres, needles, and globular polymers, hard-body amphiphilic mixtures, fluids in porous media, and random sequential adsorption that describes non-equilibrium processes such as colloidal deposition and random car parking. In these systems various physical phenomena were studied, such as correlations in liquids, freezing and demixing phase behaviour, the properties of fluid interfaces with and without orientational order, and wetting and layering phenomena at walls.

We show that classical molecular densityfunctionaltheory (MDFT), here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a fully molecular level, the solvation of complex surfaces and interfaces by polar solvents. This implicit solvent method allows for the determination of structural, orientational and energetic solvation properties that are on a par with all-atom molecular simulations performed for the same system, while reducing the computer time by two orders of magnitude. This is illustrated by the study of an atomistically-resolved clay surface composed of over a thousand atoms wetted by a molecular dipolar solvent. The high numerical efficiency of the method is exploited to carry a systematic analysis of the electrostatic and non-electrostatic components of the surface-solvent interaction within the popular CLAYFF force field. Solvent energetics and structure are found to depend weakly upon ...

Large scale DensityFunctionalTheory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.

In nuclear astro-physics, the quantum simulation of large inhomogenous dense systems as present in the crusts of neutron stars presents big challenges. The feasible number of particles in a simulation box with periodic boundary conditions is strongly limited due to the immense computational cost of the quantum methods. In this paper, we describe the techniques used to parallelize Sky3D, a nuclear densityfunctionaltheory code that operates on an equidistant grid, and optimize its performance on distributed memory architectures. We also describe cache blocking techniques to accelerate the compute-intensive matrix calculation part in Sky3D. Presented techniques allow Sky3D to achieve good scaling and high performance on a large number of cores, as demonstrated through detailed performance analysis on Edison, a Cray XC30 supercomputer.

Densityfunctionaltheory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

Time-dependent densityfunctionaltheory (TDDFT) is a reformulation of the time dependent many-body problem in quantum mechanics which is capable of reducing the computational cost to calculate, e.g., strongly driven many-electron systems enormously. Recent developments were able to overcome fundamental problems associated with ionization processes. Still vital issues have to be clarified. Besides the construction of the underlying functionals we investigate the causality problem of TDDFT by general considerations and by studying a exactly solvable system of two correlated electrons in an intense laser-pulse. For the latter system, the two alternative approaches to the construction of the action functional or a constrained functional derivative by van Leeuwen and Gal, respectively, are explored.

The minimization of the functional of the grand potential within the framework of classical densityfunctionaltheory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.

Densityfunctiontheory calculations of frequency-dependent optical rotations [α]ω for three rigid chiral molecules are reported. Calculations have been carried out at the sodium D line frequency, using the ADZP basis set and a wide variety of functionals. Gauge-invariant atomic orbitals are used to guarantee origin-independent values of [α]D. In addition, study of geometry dependence of [α]D. Is reported. Using the geometries optimized at the B3LYP/ADZP level, the mean absolute deviation of B3LYP/ADZP and experimental [α]D values yields 60.1°/(dm g/cm3). According to our knowledge, this value has not been achieved until now with any other model.

Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.

We introduced a new electron density n({\\epsilon}) by projecting the spatial electron density n(r) onto the energy coordinate {\\epsilon} defined with the external potential \\upsion (r) of interest. Then, a densityfunctionaltheory (DFT) was formulated, where n({\\epsilon}) serves as a fundamental variable for the electronic energy. It was demonstrated that the Kohn-Sham equation can also be adapted to the DFT that employs the density n({\\epsilon}) as an argument to the exchange energy functional. An important attribute of the energy density is that it involves the spatially non-local population of the spin-adapted density n(r) at the bond dissociation. By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule.

In most of the successful versions of covariant densityfunctionaltheory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in densityfunctionaltheory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact densityfunctionals is differentiable with a well-defined gradient near integer particle number.

Previous literature claims that the densityfunctionaltheory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.

Previous literature claims that the densityfunctionaltheory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.

A fundamental assumption of the dynamical densityfunctionaltheory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.

We present a hybrid densityfunctionaltheory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.

Full Text Available Amino acids are involved in many scientific theories elucidating possible origins of life on Earth. One of the challenges when discussing the evolutionary origin of biopolymers such as proteins and oligonucleotides in living organisms is the phenomenon that these polymers implement monomers of exclusively one handedness, a feature called biomolecular homochirality. Many attempts have been made to understand this process of racemic symmetry breaking. Assuming an extraterrestrial origin of the molecular building blocks of living organisms, their susceptibility to asymmetric photolysis by the absorption of circularly polarized electromagnetic radiation in interstellar space was proposed. In order to predict whether the interaction of circularly polarized light with various racemic amino acids can induce an enantiomeric excess, we investigated the electronic and chiroptical properties of the amino acids valine and isovaline by a molecular modelling approach based on quantum chemistry (DensityFunctionalTheory. The average spectra of both L-valine and L-isovaline have been produced on the basis of Boltzmann population analysis using computed spectra for the various conformations of each amino acid.

For the calculation of neutral excitations, time-dependent densityfunctionaltheory (TDDFT) is an exact reformulation of the many-body time-dependent Schroedinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schroedinger equations-the Kohn-Sham equations. The complication of the problem is hidden in the-unknown-time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe-Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.

Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent densityfunctionaltheory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.

Perdew et al. discovered two different properties of exact Kohn-Sham densityfunctionaltheory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points. (ii) Across an integer number of electrons, the exchange-correlation potential "jumps" by a constant, known as the derivative discontinuity (DD). Here we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT the two properties are two sides of the same coin. The absence of a DD dictates deviation from piecewise linearity, but the latter, appearing as curvature, can be used to correct for the former, thereby restoring the physical meaning of orbital energies. A simple correction scheme for any semilocal and hybrid functional, even Hartree-Fock theory, is shown to be effective on a set of small molecules, suggesting a practical correction for the infamous DFT gap problem. We show that optimally tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and that this can be used as a sound theoretical basis for novel tuning strategies.

We performed ab initio density-functional-theory calculations to investigate the adsorption of molecular hydrogen on pristine and Al-doped hydrogen-passivated zigzag graphene nanoribbons (GNRs) using nonlocal van der Waals functionals that have recently been proposed for an accurate description of exchange and correlation effects in weakly bound systems. Our results, which are compared with those obtained using the standard local density and generalized gradient approximations, show that neither pristine GNRs nor substitutionally Al-doped GNRs with an Al atom occupying a central, lateral, or subedge site satisfy the binding-energy criterion specified by the U.S. Department of Energy for novel hydrogen-storage materials. However, the criterion is satisfied by a GNR doped with an Al atom at an edge site and also by zigzag GNRs with adsorbed Al at lateral hole sites.

Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic densityfunctionaltheory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.

The reliability of densityfunctionaltheory (DFT) in the determination of the isotropic hyperfine coupling constants (hfccs) of the ground electronic states of organic and inorganic radicals is examined. Predictions using several DFT methods and 6-31G, TZVP, EPR-III and cc-pVQZ basis sets are made and compared to experimental values. The set of 75 radicals here studied was selected using a wide range of criteria. The systems studied are neutral, cationic, anionic; doublet, triplet, quartet; localized, and conjugated radicals, containing 1H, 9Be, 11B, 13C, 14N, 17O, 19F, 23Na, 25Mg, 27Al, 29Si, 31P, 33S, and 35Cl nuclei. The considered radicals provide 241 theoretical hfcc values, which are compared with 174 available experimental ones. The geometries of the studied systems are obtained by theoretical optimization using the same functional and basis set with which the hfccs were calculated. Regression analysis is used as a basic and appropriate methodology for this kind of comparative study. From this analysis, we conclude that DFT predictions of the hfccs are reliable for B3LYP/TZVP and B3LYP/EPR-III combinations. Both functional/basis set scheme are the more useful theoretical tools for predicting hfccs if compared to other much more expensive methods.

We revisit recent developments in the theoretical foundations of time-dependent densityfunctionaltheory (TDDFT). TDDFT is then applied to the calculation of total cross sections for ionization processes in the antiproton-Helium collision system. The Kohn-Sham potential is approximated as the sum of the Hartree-exchange potential and a correlation potential that was proposed in the context of laser-induced ionization. Furthermore, some approaches to the problem of calculating the ionization probabilities from the density are discussed. Small projectile energies below 5keV are considered as well as those in the range from 5 to 1000 keV. Results are compared with former calculations and with experimental data. We find that the correlation potential yields no obvious improvement of the results over the exchange-only approximation where the correlation potential is neglected. Furthermore, we find the problem of calculating the desired observables crucial, introducing errors of at least the same order of magnitud...

We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using densityfunctionaltheory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250-295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater.1476-112210.1038/nmat3175 10, 927 (2011) and R. T. Howie , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.125501 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.

DensityFunctionalTheory (DFT) is a powerful tool that can be used to model various systems in materials science. Our research applies DFT to two problems of interest. First, an organic/inorganic complex dye system known as a Mayan pigment is modeled to determine chemical binding sites, verifying each model with physical data such as UV/Vis spectra. Preliminary studies on palygorskite-based mayan pigments (mayacrom blue, mayacrom purple) show excellent agreement with experimental studies when using a dimer dye geometry binding with tetrahedrally-coordinated aluminum impurity sites in palygorksite. This approach is applied to a sepiolite-based organic/inorganic dye system using thioindigo attached to a tetrahedral aluminum impurity site with an additional aluminum impurity site in close proximity to the binding site. As a second application of DFT, various grain orientations in beta-Sn are modeled under imposed strains in order to calculate elastic properties of this system. These calculations are intended to clarify discrepancies in published, experimental crystal compliance values.

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in densityfunctionaltheory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragmen...

Based on the densityfunctionaltheory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 μB is observed in single Ge-chain incorporated 4 × 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices.

The spirodienone structure in lignin is a relatively recent discovery, and it has been found to occur in lignin of various plant species at concentrations of ~3%, which is sufficiently high to be important for better understanding of its properties and reactivity. The cyclic structure, with a ..beta..-1 bond, has been proposed to be a precursor for acyclic ..beta..-1 linkages in lignin. Previous analytical work has revealed the presence, but not the absolute configuration, of two stereoisomeric forms of spirodienone. The objective of the current work was to determine if there are thermodynamic differences that could help identify the experimentally observed stereoisomers. Results from densityfunctionaltheory calculations reveal the presence of clusters of stereoisomers with varying stability that may be of use in narrowing the list of possible structures. Furthermore, the bond dissociation enthalpy of the cyclic ring exhibited a particularly high value for the C-O cleavage reaction relative to more conventional ether bonds in lignin, perhaps due to limited electron delocalization possibilities.

A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using densityfunctionaltheory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).

We show that classical molecular densityfunctionaltheory, here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a fully molecular level, the solvation of complex surfaces and interfaces by polar solvents. This implicit solvent method allows for the determination of structural, orientational, and energetic solvation properties that are on a par with all-atom molecular simulations performed for the same system, while reducing the computer time by two orders of magnitude. This is illustrated by the study of an atomistically-resolved clay surface composed of over a thousand atoms wetted by a molecular dipolar solvent. The high numerical efficiency of the method is exploited to carry a systematic analysis of the electrostatic and non-electrostatic components of the surface-solvent interaction within the popular Clay Force Field (CLAYFF). Solvent energetics and structure are found to depend weakly upon the atomic charges distribution of the clay surface, even for a rather polar solvent. We conclude on the consequences of such findings for force-field development.

Ethylene epoxidation on Ag(111), Pt(111), Rh(111) and Mo(100) has been studied by densityfunctionaltheory (DFT) calculations. The results show that the adsorption energies of possible adsorbed species involved in the ethylene epoxidation increase in the order: Ag＜Pt＜Rh＜Mo, and the activation energies of the formation of epoxide (EtO) and acetaldehyde (Ac) follow the same order. Moreover, it is found that the smallest difference in the activation energies between EtO formation and Ac formation is shown on Ag. These results indicate that the metallic Ag shows the highest between activity and selectivity for ethylene epoxidation among the studied metal surfaces. Perhaps, the stability of OMME intermediate is the crucial factor in controlling the activity and selectivity. And the stronger the binding of OMME, the lower the activity and selectivity are. In addition, the relationships between the reaction enthalpy and activation energy on these four metal surfaces are investigated,and it is found that such a correlation is only applied for OMME(a) → EtO(a) and OMME(a) → Ac(a), while invalid for the case of C2H4(a) +O(a) → OMME(a).

Densityfunctionaltheory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.

By far, the most common use of time-dependent densityfunctionaltheory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states — such as the Sternheimer method — as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach.

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of densityfunctionaltheory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

There are a large number of materials with mild stiffness, which are not as soft as tissues and not as strong as metals. These semihard materials includes energetic materials, molecular crystals, layered materials, and van der Waals crystals. The integrity and mechanical stability are mainly determined by the interactions between instantaneously induced dipoles, the so called London dispersion force or van der Waals force. It is challenging to accurately model the structural and mechanical properties of these semihard materials in the frame of densityfunctionaltheory where the non-local correlation functionals are not well known. Here we propose a van der Waals densityfunctional named vdW-DFq to accurately model the density and geometry of semihard materials. Using β-cyclotetramethylene tetranitramine as a prototype, we adjust the enhancement factor of the exchange energy functional with generalized gradient approximations. We find this method to be simple and robust over a wide tuning range when calibrating the functional on-demand with experimental data. With a calibrated value q = 1 . 05 , the proposed vdW-DFq method shows good performance in predicting the geometries of 11 common energetic material molecular crystals and 3 typical layered van der Waals crystals. The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # HDTRA1-13-1-0025.

Recently, time-dependent current-densityfunctionaltheory has been extended to include the dynamical interaction of quantum systems with external environments [Phys. Rev. Lett. {\\bf 98}, 226403 (2007)]. Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems. As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the c...

Densityfunctionaltheory (DFT) is a powerful computational tool to enable structural interpretations of NMR spin-spin coupling constants ( J-couplings) in saccharides, including the abundant (1)H-(1)H ( JHH), (13)C-(1)H ( JCH), and (13)C-(13)C ( JCC) values that exist for coupling pathways comprised of 1-4 bonds. The multiple hydroxyl groups in saccharides, with their attendant lone-pair orbitals, exert significant effects on J-couplings that can be difficult to decipher and quantify without input from theory. Oxygen substituent effects are configurational and conformational in origin (e.g., axial/equatorial orientation of an OH group in an aldopyranosyl ring; C-O bond conformation involving an exocyclic OH group). DFT studies shed light on these effects, and if conducted properly, yield quantitative relationships between a specific J-coupling and one or more conformational elements in the target molecule. These relationships assist studies of saccharide structure and conformation in solution, which are often challenged by the presence of conformational averaging. Redundant J-couplings, defined as an ensemble of J-couplings sensitive to the same conformational element, are particularly helpful when the element is flexible in solution (i.e., samples multiple conformational states on the NMR time scale), provided that algorithms are available to convert redundant J-values into meaningful conformational models. If the latter conversion is achievable, the data can serve as a means of testing, validating, and refining theoretical methods like molecular dynamics (MD) simulations, which are currently relied upon heavily to assign conformational models of saccharides in solution despite a paucity of experimental data needed to independently validate the method.

We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy densityfunctional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.

The Hohenberg-Kohn theorem of DensityFunctionalTheory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

A recently proposed new family of densityfunctionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to densityfunctionaltheory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new "double hybrid" functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with approximately 500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.

We present a generalized Kohn-Sham (KS) densityfunctionaltheory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.

We present recent advances in densityfunctionaltheory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer–Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.

The effect of oxidation on the energetics and structure of thiophene (Th) oligomers is studied with densityfunctionaltheory at the B3PW91/6-311++G(d,p) level. Neutral n-Th oligomers (2 < n < 13) are gently curved planar chains. Ionization potential and electron affinity results show that n-Th oligomers are easier to be oxidized as their chain length increases. Oxidation states +2, +4, +6, and +8 are energetically stable in 12-Th. Upon oxidation the conjugated backbone of 12-Th switches from extended benzenoid phase to quinoid phase localized on groups of monomers regularly spaced along the chain. Oxidized states +2, +4, +6, and +8 of 12-Th display two +1e localized at the ends of their chains only because of the finite size of the chains. In 12-Th this end-effect extends over the two terminal monomers forming a positive-negative charge duet. This peculiar charge localization makes n-Th oligomers different from other conducting polymers with similar structure, such as polypyrrole. The spectrum of single-electron molecular states of oxidized 12-Th displays two localized single-electron states in the HOMO-LUMO energy gap per +2 oxidation state. Oligothiophene 12-Th doped with F atoms at 1:2 concentration presents a charge transfer of 3.4 e from oligomer to dopants that increases to 4.8 e in the presence of solvent. The charge distribution in these F-doped oligomers is similar to the +4 oxidation state of 12-Th. It is predicted that dopants produce an enhanced charge transfer localized in the proximity of their locations enhancing the formation of bipolarons in the central part of the oligomer chain.

Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within densityfunctionaltheory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in densityfunctionaltheory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H , with respect to a complex function F: HTC=1/F H F . It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E [n ] = ⟨Ψn|H |Ψn ⟩ /⟨Ψn|Ψn ⟩ = ⟨Dn|HTC|Dn ⟩ under the two assumptions: (1) The electron density n (r ) associated with a trial wave function Ψn = DnF is v -representable and (2) Ψn and Dn give rise to the same electron density n (r ). This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H- ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

way to very simple finite grid description of scattering and multistage conductance using time-dependent densityfunctionaltheory away from the linear regime, just as absorbing potentials and self-energies are useful for noninteracting systems and leads.

We put forward a general procedure to obtain an approximate free-energy densityfunctional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained densityfunctionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.

Presented are the results of ab-initio densityfunctional calculations for PrO2 and UO2 using the general potential LAPW and optimized LCAO method in the local density approximation. The crystal field splitting of ionic Pr4+ and U4+ ground states was calculated and compared with predictions of a superposition model.

We present a densityfunctionaltheory [M06-2X/6-31+G(d,p)] study of the structures and free energies of formation of oligomers of four carboxylic acids (formic acid, acetic acid, tetrolic acid, and benzoic acid) in water, chloroform, and carbon tetrachloride. Solvation effects were treated using the SMD continuum solvation model. The low-lying energy structures of molecular complexes were located by adopting an efficient search procedure to probe the potential energy surfaces of the oligomers of carboxylic acids (CA)n (n = 2-6). The free energies of the isomers of (CA)n in solution were determined as the sum of the electronic energy, vibrational-rotational-translational gas-phase contribution, and solvation free energy. The assessment of the computational protocol adopted in this study with respect to the dimerization of acetic acid, (AA)2, and formic acid, (FA)2, located new isomers of (AA)2 and (FA)2 and gave dimerization constants in good agreement with the experimental values. The calculation of the self-association of acetic acid, tetrolic acid, and benzoic acid shows the following: (i) Classic carboxylic dimers are the most stable isomer of (CA)2 in both the gas phase and solution. (ii) Trimers of carboxylic acid are stable in apolar aprotic solvents. (iii) Molecular clusters consisting of two interacting classic carboxylic dimers (CA)4,(D+D) are the most stable type of tetramers, but their formation from the self-association of classic carboxylic dimers is highly unfavorable. (iv) For acetic acid and tetrolic acid the reactions (CA)2 + 2CA → (CA)4,(D+D) and (CA)3 + CA → (CA)4,(D+D) are exoergonic, but these aggregation pathways go through unstable clusters that could hinder the formation of tetrameric species. (v) For tetrolic acid the prenucleation species that are more likely to form in solution are dimeric and trimeric structures that have encoded structural motifs resembling the α and β solid forms of tetrolic acid. (vi) Stable tetramers of

Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized DensityFunctionalTheory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.

Recently, time-dependent current-density-functionaltheory has been extended to include the dynamical interaction of quantum systems with external environments (Di Ventra and D'Agosta 2007 Phys. Rev. Lett. 98 226403). Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems. As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the context of quantum measurement theory.

Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for densityfunctional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for densityfunctional calculations, but the computational cost savings are a factor of about two to seven.

The computational Quantum Chemistry (QC) has been used for different types of problems, for example: structural biology, surface phenomena and liquid phase. In this paper we have employed the densityfunctional method for the study of molecular structure of loganin. The equilibrium geometry, harmonic vibrational frequencies and infrared intensities were calculated by B3LYP/6-311G (d, p) method and basis set combinations. It was found that the optimized parameters obtained by the DFT/B3LYP met...

Both electron propagator theory and density-functionaltheory provide conceptually useful information about chemical reactivity and, most especially, charge transfer. This paper elucidates thequalitative and quantitative links between the two theories, with emphasis on how the reactivity indicators of conceptual density-functionaltheory can be derived from electron propagator theory. Electron propagator theory could be used to compute reactivity indices with high accuracy at reasonable computational cost.

Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.

Full Text Available The spontaneous fission lifetimes have been studied microscopically by minimizing the collective action integral in a two-dimensional collective space of quadrupole moments (Q20, Q22 representing elongation and triaxiality. The microscopic collective potential and inertia tensor are obtained by solving the self-consistent Hartree-Fock-Bogoliubov (HFB equations with the Skyrme energy densityfunctional and mixed pairing interaction. The mass tensor is computed within the perturbative Adiabatic Time-Dependent HFB (ATDHFB approach in the cranking approximation. The dynamic fission trajectories have been obtained by minimizing the collective action using two different numerical techniques. The values of spontaneous fission lifetimes obtained in this way are compared with the static results.

We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the $T=1$ pairing condensate offers a quantitative description of the binding energy differences of open-shell superfluid nuclei. We conclude that the pairing rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing rotational moments of inertia, and demonstrate the mixing of the neutron and proton pairing rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy densityfunctional.

Full Text Available We present a densityfunctional approach to quantitatively evaluate the microscopic conformations of polymer chains with consideration of the effects of chain stiffness, polymer concentration, and short chain molecules. For polystyrene (PS, poly(ethylene oxide (PEO, and poly(methyl methacrylate (PMMA melts with low-polymerization degree, as chain length increases, they display different stretching ratios and show non-universal scaling exponents due to their different chain stiffnesses. In good solvent, increase of PS concentration induces the decline of gyration radius. For PS blends containing short (m1 = 1 − 100 and long (m = 100 chains, the expansion of long chains becomes unobvious once m 1 is larger than 40, which is also different to the scaling properties of ideal chain blends.

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation densityfunctional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to an one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.

We describe the first implementation of the all-electron Kohn-Sham densityfunctional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.

We describe the first implementation of the all-electron Kohn-Sham densityfunctional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for the nuclear potential, and an implementation for Hartree-Fock exchange.

Approximations to the exact densityfunctional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is no...

Densityfunctional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.

We present a novel implementation of Kohn-Sham density-functionaltheory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard densityfunctionals or current-densityfunctionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-densityfunctionals on the accuracy of the results. Existing current-densityfunctionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functionaltheory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

A densityfunctionaltheory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.

Aromatic interactions play a key role in many chemical and biological systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with standard wave function theory (WFT). Although densityfunctionaltheory (DFT) can easily treat systems of more than 200 atoms, standard semilocal (hybrid) densityfunctional approximations fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramolecular noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the investigation and analysis of a wide range of complex aromatic systems. In this Account, we start with an analysis of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The minima for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of saturated and aromatic model complexes, we show that increased dispersion coefficients for sp(2)-hybridized carbon atoms play a major role in aromatic stacking. Modern dispersion-corrected DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate reference data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, density-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramolecular interactions that arise in the molecular crystals of aromatic molecules. In studies of hexahelicene, dispersion-corrected DFT yields "the right answer for the right reason". By comparison, standard DFT calculations reproduce intramolecular distances quite

The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well as long-range isotropic and anisotropic elasticity, (iii) a closed-form stress expression accounting for the nonlocal molecular interaction, and (iv) an extra elastic body force exclusively associated with the integral form of the intermolecular potential. With the effective intermolecular potential, the theory is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics. Approximate theories are obtained by gradient expansions of the number densityfunction in the free energy density.

Recent advances in the understanding of reactivity trends for chemistry at transition metal surfaces have enabled in silico design of heterogeneous catalysts in a few cases. Current status of the field is discussed with an emphasis on the role of coupling between theory and experiment and future challenges.

Recent advances in the understanding of reactivity trends for chemistry at transition-metal surfaces have enabled in silico design of heterogeneous catalysts in a few cases. The current status of the field is discussed with an emphasis on the role of coupling theory and experiment and future...

We present a novel implementation of Kohn–Sham density-functionaltheory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard densityfunctionals or current-density functionals—the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-densityfunctionals on the accuracy of the results. Existing current-densityfunctionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functionaltheory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

We discuss two problems which are particularly challenging for approximations in time-dependent densityfunctionaltheory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We propose an extension of TDDFT to phase-space densities, discuss some formal aspects of such a "phase-space densityfunctionaltheory" and explain why it could ameliorate the problems in both cases. For each problem, a two-electron model system is exactly nume...

We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.......We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....

A general class of nonlocal cosmological models is considered. A new method for solving nonlocal Friedmann equations is proposed, and solutions of the Friedmann equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed. Especially indicated is $p$-adic cosmological model in which we have obtained nonsingular bouncing solution and string field theory tachyon model in which we have obtained full solution of nonlocal Friedmann equations with $w=...

Time-dependent densityfunctionaltheory (TDDFT) is an exact reformulation of the time-dependent many-electron Schroedinger equation, where the problem of many interacting electrons is mapped onto the Kohn-Sham system of noninteracting particles which reproduces the exact electronic density. In the Kohn-Sham system all non-classical many-body effects are incorporated in the exchange-correlation potential which is in general unknown and needs to be approximated. It is the goal of this thesis to investigate the connection between memory effects and correlated electron dynamics in strong and weak fields. To this end one-dimensional two-electron singlet systems are studied. At the same time these systems include the onedimensional helium atom model, which is an established system to investigate the crucial effects of correlated electron dynamics in external fields. The studies presented in this thesis show that memory effects are negligible for typical strong field processes. Here the approximation of the spatial nonlocality is of primary importance. For the photoabsorption spectra on the other hand the neglect of memory effects leads to qualitative and quantitative errors, which are shown to be connected to transitions of double excitation character. To develop a better understanding of the conditions under which memory effects become important quantum fluid dynamics has been found to be especially suitable. It represents a further exact reformulation of the quantum mechanic many-body problem which is based on hydrodynamic quantities such as density and velocity. Memory effects are shown to be important whenever the velocity field develops strong gradients and dissipative effects contribute. (orig.)

Full Text Available The purpose of this paper is to explain why the standard continuum theory fails to properly describe certain mechanical phenomena and how the description can be improved by enrichments that incorporate the influence of gradients or weighted spatial averages of strain or of an internal variable. Three typical mechanical problems that require such enrichments are presented: (i dispersion of short elastic waves in heterogeneous or discrete media, (ii size effects in microscale elastoplasticity, in particular with the size dependence of the apparent hardening modulus, and (iii localization of strain and damage in quasibrittle structures and with the resulting transitional size effect. Problems covered in the examples encompass static and dynamic phenomena, linear and nonlinear behavior, and three constitutive frameworks, namely elasticity, plasticity and continuum damage mechanics. This shows that enrichments of the standard continuum theory can be useful in a wide range of mechanical problems.

A correct description of electronically excited states is critical to the interpretation of visible-ultraviolet spectra, photochemical reactions, and excited-state charge-transfer processes in chemical systems. We have recently proposed a theory called multiconfiguration pair-densityfunctionaltheory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory and a new kind of densityfunctional called an on-top densityfunctional. Here, we show that MC-PDFT with a first-generation on-top densityfunctional performs as well as CASPT2 for an organic chemistry database including valence, Rydberg, and charge-transfer excitations. The results are very encouraging for practical applications.

A modified non-local free energy densityfunctionaltheory (NDFT) model, with the consideration of the nonadditivity term of solid-fluid and fluid-fluid interactions and finite pore wall thickness (≈2 layers), was developed to model the confined fluid mixtures in slit pore. This improved NDFT approach, com-bining with the pore size distribution (PSD) analysis of adsorbent material can be applied to predicting the adsorption equilibria of high-pressure gas mixtures on activated carbon. Compared with the con-ventional NDFT method, this new approach partly improves the correlation performance of adsorption equilibrium for pure species and increases the reliability of the PSD analysis. For the mixtures, CH4/N2 and CO2/N2, a relatively improved performance has been observed for the adsorption equilibrium pre-diction of the mixtures under high-pressure conditions, especially for the weakly adsorbed species.

Densityfunctionaltheory (DFT) and x-ray absorption fine structure (XAFS) spectroscopy are complementary tools for the biophysical study of active sites in metalloproteins. DFT is used to compute XAFS multiple scattering Debye Waller factors, which are then employed in genetic algorithm-based fitting process to obtain a global fit to the XAFS in the space of fitting parameters. Zn-Cys sites, which serve important functions as transcriptional switches in Zn finger proteins and matrix metalloproteinases, previously have proven intractable by this method; here these limitations are removed. In this work we evaluate optimal DFT nonlocal functionals and basis sets for determining optimal geometries and vibrational densities of states of mixed ligation Zn(His)4-n(Cys)n sites. Theoretical results are compared to experimental XAFS measurements and Raman spectra from the literature and tabulated for use.

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of DensityFunctionalTheory (DFT) for periodic systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within chemical accuracies. We demonstrate using a wide variety of materials systems that SPARC obtains high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; energies and forces that are consistent and display negligible `egg-box' effect; and accurate ground-state properties. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementa...

As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of DensityFunctionalTheory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within chemical accuracies. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable `egg-box' effect; and accurate ground-state properties includin...

Densityfunctionaltheory (DFT) and x-ray absorption fine structure (XAFS) spectroscopy are complementary tools for the biophysical study of active sites in metalloproteins. DFT is used to compute XAFS multiple scattering Debye Waller factors, which are then employed in genetic algorithm-based fitting process to obtain a global fit to the XAFS in the space of fitting parameters. Zn-Cys sites, which serve important functions as transcriptional switches in Zn finger proteins and matrix metalloproteinases, previously have proven intractable by this method; here these limitations are removed. In this work we evaluate optimal DFT nonlocal functionals and basis sets for determining optimal geometries and vibrational densities of states of mixed ligation Zn(His)(4-n)(Cys)(n) sites. Theoretical results are compared to experimental XAFS measurements and Raman spectra from the literature and tabulated for use.

We present a general and formally exact method to obtain the canonical one-body density distribution and the canonical free energy from direct decomposition of classical densityfunctional results in the grand ensemble. We test the method for confined one-dimensional hard-core particles for which the exact grand potential densityfunctional is explicitly known. The results agree to within high accuracy with those from exact methods and our Monte Carlo many-body simulations. The method is relevant for treating finite systems and for dynamical densityfunctionaltheory.

The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio densityfunctionaltheory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non-local

The electric field gradient (EFG) at the nucleus, the generalized Sternheimer shielding constants, and the EFG hyperpolarizabilities of a set of reference molecules are computed using analytic density-functional (up to quadratic) response theory. At the three-parameter Becke-Lee-Yang-Parr (B3LYP) level, densityfunctionaltheory (DFT) underestimates correlation effects compared with other approaches such as coupled-cluster and multiconfigurational self-consistent field. For the prediction of EFG properties of hydrogen nuclei and electron-rich atoms such as halides, DFT/B3LYP provides results even less reliable than Hartree-Fock theory.

Microporous sorbents such as carbons, silicas and aluminas are used commercially in a variety of separation, purification and selective reaction applications. A detailed study of the effects of the porous material characteristics on the adsorption equilibrium properties such as selectivity and phase equilibria of fluid mixtures can enhance our understanding of adsorption on a molecular level. Such knowledge will improve our utilization of such adsorbents and provide a tool for directing the future of tailoring sorbents for particular separation processes. The effect of pore size, shape and pressure on the selective adsorption of trace pollutants from an inert gas was studied using prototype mixtures of Lennard-Tones (LJ) N2/CCl4, CF4, and SO2. Both nonlocaldensityfunctionaltheory (DFT) and grand canonical Monte Carlo (GCMC) molecular simulations were used in order to investigate the validity of the theory, which is much quicker and easier to use. Our results indicate that there is an optimal pore size and shape for which the pollutant selectivity is greatly enhanced. In many industrial adsorption processes relative humidity can greatly affect the life of an adsorbent bed, as seen in breakthrough curves. Therefore, the influence of water vapor on the selective adsorption of CCl4 from a mixture of N2/CCl4/H20 in activated carbon was studied using GCMC simulations. The equilibrium adsorption properties are found to be dependent upon both the density of active sites on the pore walls and the relative humidity. Liquid-liquid transitions in porous materials are of interest in connection with oil recovery, lubrication, coating technology and pollution control. The results of a study on the effect of confinement on the liquid-liquid equilibrium of binary LJ mixtures using DFT are compared with those of molecular simulation and experiments. Our findings show that the phase coexistence for the confined mixture is in general decreased and shifted toward the component which

A densityfunctionaltheory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods

A densityfunctionaltheory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods

A densityfunctionaltheory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT

Kohn-Sham densityfunctionaltheory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-densityfunctionaltheory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a densityfunctional, called the on-top densityfunctional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top densityfunctional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable densityfunctional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.

This book is an outcome of the International Workshop on Electronic DensityFunctionalTheory, held at Griffith University in Brisbane, Australia, in July 1996. Densityfunctionaltheory, standing as it does at the boundary between the disciplines of physics, chemistry, and materials science, is a great mixer. Invited experts from North America, Europe, and Australia mingled with students from several disciplines, rapidly taking up the informal style for which Australia is famous. A list of participants is given at the end of the book. Densityfunctionaltheory (DFT) is a subtle approach to the very difficult problem of predicting the behavior of many interacting particles. A major application is the study of many-electron systems. This was the workshop theme, embracing inter alia computational chemistry and condensed matter physics. DFT circumvents the more conceptually straightforward (but more computationally intensive) approach in which one solves the many-body Schrodinger equation. It relies instead on r...

The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical densityfunctionaltheories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced. To facilitate a more natural way of binding together the dynamics of the macrovariables and classical densityfunctionaltheory, a dynamic generalization of densityfunctionaltheory based on the nonequilibrium generating functional is suggested.

A combinatorially optimized, range-separated hybrid, meta-GGA densityfunctional with VV10 nonlocal correlation is presented. The final 12-parameter functional form is selected from approximately 10 × 109 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting densityfunctional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading densityfunctionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested densityfunctionals. In order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided.

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functionaltheory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functionaltheory and time-dependent density-functionaltheory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

We present PROFESS (PRinceton Orbital-Free Electronic Structure Software), a new software package that performs orbital-free densityfunctionaltheory (OF-DFT) calculations. OF-DFT is a first principles quantum mechanics method primarily for condensed matter that can be made to scale linearly with system size. We describe the implementation of energy, force, and stress functionals and the methods used to optimize the electron density under periodic boundary conditions. All electronic energy and potential terms scale linearly while terms involving the ions exhibit quadratic scaling in our code. Despite the latter scaling, the program can treat tens of thousands of atoms with quantum mechanics on a single processor, as we demonstrate here. Limitations of the method are also outlined, the most serious of which is the accuracy of state-of-the-art kinetic energy functionals, which limits the applicability of the method to main group elements at present. Program summaryProgram title: PROFESS Catalogue identifier: AEBN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 35 933 No. of bytes in distributed program, including test data, etc.: 329 924 Distribution format: tar.gz Programming language: Fortran 90 Computer: Intel with ifort; AMD Opteron with pathf90 Operating system: Linux RAM: Problem dependent, but 2 GB is sufficient for up to 10,000 ions Classification: 7.3 External routines: FFTW ( http://www.fftw.org), MINPACK-2 Nature of problem: Given a set of coordinates describing the initial ion positions under periodic boundary conditions, recovers the ground state energy, electron density, ion positions, and cell lattice vectors predicted by orbital-free densityfunctionaltheory. Except for computation of the

We propose an approach to perform orbital-free densityfunctionaltheory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free densityfunctionaltheory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.

We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.

We present the basic concepts and our recent developments in the densityfunctional approaches with the Skyrme functionals for describing nuclear dynamics at low energy. The time-dependent density-functionaltheory (TDDFT) is utilized for the exact linear response with an external perturbation. For description of collective dynamics beyond the perturbative regime, we present a theory of a decoupled collective submanifold to describe for a slow motion based on the TDDFT. Selected applications are shown to demonstrate the quality of their performance and feasibility. Advantages and disadvantages in the numerical aspects are also discussed.

We study the ϕ4 field theory in d = 4. Using bold diagrammatic Monte Carlo method, we solve the Schwinger-Dyson equations and find the spectral densityfunction of the theory beyond the weak coupling regime. We then compare our result with the one obtained from the perturbation theory. At the end, we utilize our Monte Carlo result to find the vertex function as the basis for the computation of the physical scattering amplitudes.

Standard densityfunctional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected densityfunctionaltheory (DC-DFT), certain classes of densityfunctionaltheory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl(-) and HO·H2O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.

Due to the large value of the scattering length in nuclear systems, standard density--functionaltheories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme densityfunctional and, on the other side, by resummation techniques used in Effective Field Theories for systems with large scattering lengths, a new energy--densityfunctional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.

Standard densityfunctional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected densityfunctionaltheory (DC-DFT), certain classes of densityfunctionaltheory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO$\\cdot$Cl$^-$ and HO$\\cdot$H$_2$O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.

The sources of error in the calculation of nuclear-magnetic-resonance shielding constants determined by density-functionaltheory are examined. Highly accurate Kohn-Sham wave functions are obtained from coupled-cluster electron densityfunctions and used to define accurate-but current independent-density-functional shielding constants. These new reference values, in tandem with high-accuracy coupled-cluster shielding constants, provide a benchmark for the assessment of errors in common density-functional approximations. In particular the role of errors arising in the diamagnetic and paramagnetic terms is investigated, with particular emphasis on the role of current-dependence in the latter. For carbon and nitrogen the current correction is found to be, in some cases, larger than 10 ppm. This indicates that the absence of this correction in general purpose exchange-correlation functionals is one of the main sources of error in shielding calculations using densityfunctionaltheory. It is shown that the current correction improves the shielding performance of many popular approximate DFT functionals.

Full Text Available The possible eight rotamers of 3′-Methyl-quercetin have been optimized by using densityfunctionaltheory (DFT at B3LYP/6-31G∗ level of theory. The molecular structure and molecular properties of the most stable rotamers have been investigated at the same level of theory. We have computed the descriptors; electronegativity (χ, hardness (η, electrophilicity (ω, softness (S and electrophilicity index (ωi by DFT approach. We have shed light on the structure–property relationship. The absorption spectrum has been computed by time dependent densityfunctionaltheory (TD-DFT at TD-B3LYP/6-31G∗ level of theory. Radical scavenging activity has been explained on the basis of bond dissociation enthalpy (BDE and the adiabatic ionization potential (IP. Two mechanisms have been explained for the radical scavenging processes, i.e., hydrogen atom transfer and one-electron transfer.

Patulin, a secondary metabolite produced by several fungal species, is a potential contaminant of fruit and vegetable products. To better understand the structure and electronic properties of this mycotoxin and its biosynthetic precursors, a densityfunctionaltheory (DFT) study was performed on co...

The hyperfine structure and isotope shifts of Sr-isotopes, both even-even and odd-even nuclei, are studied in the covariant densityfunctionaltheory (DFT) with the new parameter set DD-PC1. Pairing correlation is treated by using the Bogoliubov with a separable form of the pairing interaction. Spin-parity,

Many drug compounds are oxidized by cytochrome P450 (CYP) enzymes to form reactive metabolites. This study presents densityfunctionaltheory calculations of the CYP-mediated metabolism of acetaminophen and a series of related compounds that can form reactive metabolites by hydrogen abstraction...

We extend the formulation of time-dependent current-density-functionaltheory for the linear response properties of dielectric and semi-metallic solids [Kootstra , J. Chem. Phys. 112, 6517 (2000)] to treat metals as well. To achieve this, the Kohn-Sham response functions have to include both interba

Mechanisms and energetics of graphene growth catalyzed by nickel nanoclusters were studied using ab initio densityfunctionaltheory calculations. It is demonstrated that nickel step-edge sites act as the preferential growth centers for graphene layers on the nickel surface. Carbon is transported...

We extend the formulation of time-dependent current-density-functionaltheory for the linear response properties of dielectric and semi-metallic solids [Kootstra , J. Chem. Phys. 112, 6517 (2000)] to treat metals as well. To achieve this, the Kohn-Sham response functions have to include both

We study the oxygen reduction reaction (ORR) mechanism on a Pt(1 1 1) surface using densityfunctionaltheory calculations We find that at low overpotentials the surface is covered with a half dissociated water layer We estimate the barrier for proton transfer to this surface and the barrier for ...

to analyze diffraction effects on the amplitude and the phase. There is relatively good comparison between image simulation and experimental data, but the experimental absorption parameter is found to differ between strongly and weakly diffracting conditions. Densityfunctionaltheory simulations of the mean...

We present the implementation of the time-dependent density-functionaltheory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we...

In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-densityfunctionaltheory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this

series of (pseudo)cubic perovskites, ABO3, have been investigated using densityfunctionaltheory calculations. The structures have been optimized and thermodynamic properties and activation energies for the relevant steps of the hydrogen/proton diffusion mechanism have been calculated using...

We have used densityfunctionaltheory to predict the ion exchange energies for divalent cations Ni(2+), Sr(2+), Cd(2+), and Pb(2+) into a calcite {10.4} surface in equilibrium with water. Exchange energies were calculated for substitution into the topmost surface layer, at the mineral...

Densityfunctionaltheory (DFT) is a type of electronic structure calculation that has rapidly gained popularity. In this article, we provide a step-by-step demonstration of a DFT calculation by hand on the helium atom using Slater's X-Alpha exchange functional on a single Gaussian-type orbital to represent the atomic wave function. This DFT…

The geometry of tetracyanoplatinate(II) (TCP) has been optimized with densityfunctionaltheory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...

It is known that the edges of a two-dimensional slab of insulating MoS2 exhibit one-dimensional metallic edge states, the so-called "brim states." Here, we find from density-functionaltheory calculations that several edge structures, which are relevant for the hydrodesulfurization process, are m...

One component hard-sphere fluid confined in two planar hard walls is studied by means of densityfunctionaltheory with Rosenfeld functional and molecular dynamics simulation. The validity of the Rosenfeld functional is examined. Chemical potential, grand potential and free energy as functions of the wall separation are obtained.

The core structures of (I 11) screw dislocations in bee metals are studied using densityfunctionaltheory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180degrees rotations around an axis perpendicular...

In this study densityfunctionaltheory (DFT) was used to study the adsorption of guaiacol and its initial hydrodeoxygenation (HDO) reactions on Pt(111). Previously reported Brønsted–Evans–Polanyi (BEP) correlations for small open chain molecules are found to be inadequate in estimating the reaction...

The present paper reports the study of phonon properties of a two dimensional antimony nanosheet under the biaxial strain using first principles calculation based on densityfunctionaltheory. Our calculations shows that the strain turns the quadratic dependence of wave vector on frequency to the linear dependency which can be linked with the removal of rippling in nanosheets.

equation (25)). The constants c1 and c2 which correspond to the scaling and shifting are determined such that the unwanted eigen-spectrum is mapped into...U. Gross, A. Rubio, Octopus : A tool for the application of time- dependent densityfunctionaltheory, Phys. Status Solidi B 243 (2006) 24652488. [12

We present densityfunctionaltheory calculations of the adsorption of arsenic acid (AsO(OH)3) and arsenous acid (As(OH)3) on the Al(III)-modified natural zeolite clinoptilolite under anhydrous and hydrated conditions. From our calculated adsorption energies, we show that adsorption of both arsenic

We present densityfunctionaltheory calculations of the adsorption of arsenic acid (AsO(OH)3) and arsenous acid (As(OH)3) on the Al(III)-modified natural zeolite clinoptilolite under anhydrous and hydrated conditions. From our calculated adsorption energies, we show that adsorption of both arsenic

Densityfunctionaltheory (DFT) is a type of electronic structure calculation that has rapidly gained popularity. In this article, we provide a step-by-step demonstration of a DFT calculation by hand on the helium atom using Slater's X-Alpha exchange functional on a single Gaussian-type orbital to represent the atomic wave function. This DFT…

Citrinin is a toxic polyketide contaminant of a number of agricultural commodities, notably Monascus-fermented red rice. Detailed structures and electronic properties of three tautomeric forms of citrinin were investigated using densityfunctionaltheory calculations at various extended basis sets ...

A method for improving the electronic spectrum of standard Density-FunctionalTheory (DFT) calculations (i.e., LDA or GGA approximations) is presented, and its application is discussed for the case of the copper phthalocyanine (CuPc) molecule. The method is based on a treatment of exchange and co...

We examine the application of the recently developed dual basis methods of Head-Gordon and co-workers to double hybrid densityfunctional computations. Using the B2-PLYP, B2GP-PLYP, DSD-BLYP and DSD-PBEP86 densityfunctionals, we assess the performance of dual basis methods for the calculation of conformational energy changes in C$_4$-C$_7$ alkanes and for the S22 set of noncovalent interaction energies. The dual basis methods, combined with resolution-of-the-identity second-order M{\\o}ller-Plesset theory, are shown to give results in excellent agreement with conventional methods at a much reduced computational cost.

The terahertz time-domain spectrum (THz-TDS) of chlorotoluron has been simulated and assigned with solid-state densityfunctionaltheory (DFT) in the range of 0.5-2.2 THz. The calculations based on the hybrid densityfunctionals B3LYP and PW91 are performed to analyze the origins of observed spectral features in chlorotoluron THz spectra of solid-state forms using the software package CRYSTAL09. The computed THz spectrum of the B3LYP provides better agreements with observed THz spectral characters. Moreover, all the experimental THz absorption peaks are assigned utilizing the B3LYP method.

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy densityfunctional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.

Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Moebius functions of partially ordered sets. The free-energy densityfunctional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Moebius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.

All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the densityfunctional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these equations which are satisified by the correct kernels, which guarantee a unique solution to the integral equations, and which provide a natural constraint on approximations which can be used in densityfunctionaltheory. It is also shown that this sensitive behavior is a general property of densityfunctional problems and that the methodology for constructing the constraints is equally general. A variety of applications of densityfunctionaltheory are reviewed to illustrate practical consequences of this sensitivity.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on densityfunctionaltheory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital densityfunctional tight binding (FODFTB) method gives similar results to constrained densityfunctionaltheory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on densityfunctionaltheory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital densityfunctional tight binding (FODFTB) method gives similar results to constrained densityfunctionaltheory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

Classical densityfunctionaltheory (DFT) for fluids and its dynamic extension (DDFT) provide an appealing mean-field framework for describing equilibrium and dynamics of complex soft matter systems. For a long time, homogeneous nucleation was considered to be outside the limits of applicability of DDFT. However, our recently developed mesoscopic nucleation theory (MeNT) based on fluctuating hydrodynamics, reconciles the inherent randomness of the nucleation process with the deterministic nature of DDFT. It turns out that in the weak-noise limit, the most likely path (MLP) for nucleation to occur is determined by the DDFT equations. We present computations of MLPs for homogeneous and heterogeneous nucleation in colloidal suspensions. For homogeneous nucleation, the MLP obtained is in excellent agreement with the reduced order-parameter description of MeNT, which predicts a multistage nucleation pathway. For heterogeneous nucleation, the presence of impurities in the fluid affects the MLP, but remarkably, the overall qualitative picture of homogeneous nucleation persists. Finally, we highlight the use of DDFT as a simulation tool, which is especially appealing as there are no known applications of MeNT to heterogeneous nucleation. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from EPSRC via Grants No. EP/L020564 and EP/L025159.

Linear-scaling quantum mechanical densityfunctionaltheory calculations have been applied to study the rearrangement of chorismate to prephenate in large-scale models of the Bacillus subtilis chorismate mutase enzyme. By treating up to 2000 atoms at a consistent quantum mechanical level of theory, we obtain an unbiased, almost parameter-free description of the transition state geometry and energetics. The activation energy barrier is calculated to be lowered by 10.5 kcal mol(-1) in the enzyme, compared with the equivalent reaction in water, which is in good agreement with experiment. Natural bond orbital analysis identifies a number of active site residues that are important for transition state stabilization in chorismate mutase. This benchmark study demonstrates that linear-scaling densityfunctionaltheory techniques are capable of simulating entire enzymes at the ab initio quantum mechanical level of accuracy.

Time-dependent (current) densityfunctionaltheory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent densityfunctionaltheory for systems coupled to the Caldeira-Leggett bath.

The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular densityfunctionaltheory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. With this correction, molecular densityfunctionaltheory gives, at a modest computational cost, quantita...

This proceeding is based on a talk prepared for the XIV Marcel Grossmann meeting. We review some results on causal set inspired non-localtheories as well as work in progress concerning their phenomenology.

In the semiconductor industry, the use of new materials has been increasing with the advent of nanotechnology. As critical dimensions decrease, and the number of materials increases, the interactions between heterogeneous materials themselves and processing increase in complexity. Traditionally, applications of ab initio techniques are confined to electronic structure and band gap calculations of bulk materials, which are then used in coarse-grained models such as mesoscopic and continuum models. Densityfunctionaltheory is the most widely used ab initio technique that was successfully extended to several applications. This paper illustrates applications of densityfunctionaltheory to semiconductor processes and proposes further opportunities for use of such techniques in process development.

The concept of quantum electronic stress (QES) is introduced and formulated within densityfunctionaltheory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σ(QE)) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σ(QE) = ΞΔn as a quantum analog of classical Hooke's law. Two distinct QES manifestations are demonstrated quantitatively by densityfunctionaltheory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functionaltheory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functionaltheory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

We report the implementation of a two-component variant of time-dependent densityfunctionaltheory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure densityfunctionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.

This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of densityfunctionaltheory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in densityfunctionaltheory. The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research. Readership: Graduate students, academics and researchers in computational chemistry. Atomic & molecular physicists, theoretical physicists, theoretical chemists, physical chemists and chemical physicists.

Recently, electron transport properties of molecular junctions under finite bias voltages have attracted a lot of attention because of the potential application of molecular electronic devices. When a molecular junction is under zero bias voltage at zero temperature, it is in equilibrium ground state and all its properties can be solved by ground-state densityfunctionaltheory (GS-DFT) where ground-state electron density determines everything. Under finite bias voltage, the molecular junction is in non-equilibrium steady state. According to Hershfield's non-equilibrium statistics, a system in non-equilibrium steady state corresponds to an effective equilibrium system. This correspondence provides the basis for the steady-state densityfunctionaltheory (SS-DFT) which will be developed in this thesis. (Abstract shortened by UMI.).

The concept of quantum electronic stress (QES) is introduced and formulated within densityfunctionaltheory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σQE) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σQE=ΞΔn as a quantum analog of classical Hooke’s law. Two distinct QES manifestations are demonstrated quantitatively by densityfunctionaltheory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.

The exact conditions for densityfunctionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate densityfunctionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the

@@ Thioaldehydes and thioketones are candidates of new photoluminescence materials. The time-dependent densityfunctionaltheory is applied to calculate the absorption and emission wavelengths of ten thiocarbonyl compounds using both B3LYP and PBE0 functionals. The theoretical results are in agreement with the measurable ones.Furthermore, it is found that the maximum absorption and emission wavelengths are linearly correlated to the C-S bond lengths.

In this lecture, we will present some nucleonic equations of state of neutron-star matter calculated within the nuclear energy-densityfunctionaltheory using generalized Skyrme functionals developed by the Brussels-Montreal collaboration. These equations of state provide a consistent description of all regions of a neutron star. The global structure of neutron stars predicted by these equations of state will be discussed in connection with recent astrophysical observations.

quantitatively and non-empirically within the framework of time-dependent densityfunctionaltheory (TDDFT), using the recently-developed optimally-tuned...showing that fundamental gaps and optical spectra of molecular solids can be predicted quantitatively and non-empirically within the framework of...II. THEORETICAL AND COMPUTATIONAL APPROACH A. Optimally-tuned range-separated hybrid functionals In the range-separated hybrid (RSH) method, the

For ammonia synthesis catalysts a volcano-type relationship has been found experimentally. We demonstrate that by combining densityfunctionaltheory calculations with a microkinetic model the position of the maximum of the volcano curve is sensitive to the reaction conditions. The catalytic ammo......-principle quantum mechanical calculations of gas-surface interactions, reactor design, and catalyst selection has been established for the first time....

Phonon frequencies at {\\Gamma},X,M,R-points of Brilloin zone in cubic phase of Ba(Ti,Zr,Hf)O3 were first time calculated by frozen phonon method using densityfunctionaltheory (DFT) with hybrid exchange correlation functional PBE0. The calculations use linear combination of atomic orbitals (LCAO) basis functions as implemented in CRYSTAL09 computer code. The Powell algorithm was applied for basis set optimization. In agreement with the experimental observations the structural instability via...

A comparison of the ab initio quantum chemical methods: Hartree-Fock (HF) and hybrid densityfunctionaltheory (DFT)/B3LYP for the treatment of tautomeric equilibria both in the gas phase and in the solution is made. The solvent effects were investigated in terms of the self-consistent reaction field (SCRF). Ionization potentials (IP), calculated by DFT/B3LYP, are also compared with those calculated previously within the HF frame.

Theoretical reactivity indices based on the conceptual DensityFunctionalTheory (DFT) have become a powerful tool for the semiquantitative study of organic reactivity. A large number of reactivity indices have been proposed in the literature. Herein, global quantities like the electronic chemical potential μ, the electrophilicity ω and the nucleophilicity N indices, and local condensed indices like the electrophilic P k + and nucleophilic P k - Parr functions, as the most relevant indices for the study of organic reactivity, are discussed.

We describe an iterative algorithm to solve electronic structure problems in DensityFunctionalTheory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.

International audience; We present a three-dimensional molecular densityfunctionaltheory of water derived fromfirst-principles that relies on the particle’s density and multipolar polarization density andincludes the density–polarization coupling. This brings two main benefits: (i) scalar densityand vectorial multipolar polarization density fields are much more tractable and give morephysical insight than the full position and orientation densities, and (ii) it includes the fulldensity–pola...

By applying time-dependent densityfunctionaltheory to a two-dimensional multielectron atom subject to strong circularly polarized light pulses, we confirm that the ionization of p orbitals with defined angular momentum depends on the sense of rotation of the applied field. A simple ad-hoc modification of the adiabatic local-density exchange-correlation functional is proposed to remedy its unphysical behavior under orbital depletion.

A screening study of the steam reforming reaction on clean and oxygen covered early transition-metal carbides surfaces is performed by means of density-functionaltheory calculations. It is found that carbides provide a wide spectrum of reactivities, from too reactive via suitable to too inert. Several molybdenum-based systems are identified as possible steam reforming catalysts. The findings suggest that carbides provide a playground for reactivity tuning, comparable to the one for pure metals.

The optical properties of Al nanostructures are investigated by means of time dependent densityfunctionaltheory, considering chains of varying length and ladders/stripes of varying aspect ratio. The absorption spectra show redshifting for increasing length and aspect ratio. For the chains the absorption is dominated by HOMO → LUMO transitions, whereas ladders and stripes reveal more complex spectra of plasmonic nature above a specific aspect ratio.

International audience; Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order M{{\\o}}ller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, m...

The correction of the self-interaction error (SIE) that is inherent to all standard densityfunctionaltheory (DFT) calculations is an object of increasing interest. In this article we apply the very recently developed Fermi-orbital based approach for the self-interaction correction (FOSIC) to a set of different molecular systems. Our study covers systems ranging from simple diatomic to large organic molecules. We focus our analysis on the direct estimation of the ionization potential from orbital eigenvalues.

This paper overviews various phenomena related to the concept of isospin symmetry. The focus is on N~Z nuclei, which are excellent laboratories of isospin physics. The theoretical framework applied is nuclear DensityFunctionalTheory and its isospin- and angular-momentum projected extensions, as well as symmetry-projected multi-reference models. The topics covered include: isospin impurities, superallowed beta decays, beta-transitions in mirror nuclei, isospin breaking hadronic interactions, mirror and triplet binding energy differences, and isoscalar pairing.

Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.

Time-dependent Kohn-Sham densityfunctionaltheory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-densityfunctionaltheory (MC-PDFT). We use the tPBE on-top densityfunctional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.

A general densityfunctionaltheory/molecular mechanics approach for computation of electronic g-tensors of solvated molecules is presented. We apply the theory to the commonly studied di-tert-butyl nitroxide molecule, the simplest model compound for nitroxide spin labels, and explore the role of an aqueous environment and of various approximations for its treatment. It is found that successive improvements of the solvent shift of the g-tensor are obtained by going from the polarizable continuum model to discrete solvent models of various levels of sophistication. The study shows that an accurate parametrization of the electrostatic potential and polarizability of the solvent molecules in terms of distributed multipole expansions and anisotropic polarizabilities to a large degree relieves the need to explicitly include water molecules in the quantum region, which is the common case in densityfunctional/continuum model approaches. It is also shown that the local dynamics of the solvent around the solute significantly influences the electronic g-tensor and should be included in benchmarking of exchange-correlation functionals for evaluation of solvent shifts of g-tensors. These findings can have important ramifications for the use of advanced hybrid densityfunctionaltheory/molecular mechanics approaches for modeling spin labels in solvents, proteins, and membrane environments.

In recent years, a number of dynamical densityfunctionaltheories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is overdamped and also in the regime where inertial effects are relevant. In this paper, we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation, which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalization of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium densityfunctionaltheory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.

We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.

We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.

The electronic properties of LiCoO2 have been studied by theoretical band-structure calculations (using densityfunctionaltheory) and experimental methods (photoemission). Synchrotron-induced photoelectron spectroscopy, resonant photoemission spectroscopy (ResPES), and soft x-ray absorption (XAS) have been applied to investigate the electronic structure of both occupied and unoccupied states. High-quality PES spectra were obtained from stoichiometric and highly crystalline LiCoO2 thin films deposited “in situ” by rf magnetron sputtering. An experimental approach of separating oxygen- and cobalt-derived (final) states by ResPES in the valence-band region is presented. The procedure takes advantage of an antiresonant behavior of cobalt-derived states at the 3p-3d excitation threshold. Information about the unoccupied density of states has been obtained by OK XAS. The structure of the CoL absorption edge is compared to semiempirical charge-transfer multiplet calculations. The experimental results are furthermore compared with band-structure calculations considering three different exchange potentials [generalized gradient approximation (GGA), using a nonlocal Hubbard U (GGA+U) and using a hybrid functional (Becke, three-parameter, Lee-Yang-Parr [B3LYP])]. For these different approaches total density of states and partial valence-band density of states have been investigated. The best qualitative agreement with experimental results has been obtained by using a GGA+U functional with U=2.9eV .

We present an accurate and efficient technique for calculating thermal X-ray absorption fine structure (XAFS) Debye-Waller factors (DWFs) applicable to crystalline materials. Using DensityFunctionalTheory on a 3x3x3 supercell pattern of MnO structure, under the nonlocal hybrid B3LYP functional paired with Gaussian local basis sets, we obtain the normal mode eigenfrequencies and eigenvectors; these parameters are in turn used to calculate single and multiple scattering XAFS DWFs. The DWFs obtained via this technique are temperature dependent expressions and can be used to substantially reduce the number of fitting parameters, when experimental spectra are fitted with a hypothetical structure. The size of the supercell size limits the R-space range that these parameters could be used. Therefore corresponding DWFs for paths outside of this range are calculated using the correlated Debye model. Our method is compared with prior cluster calculations and with corresponding values obtained from fitting experimental XAFS spectra on manganosite with simulated spectra.

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of DensityFunctionalTheory (DFT) for extended systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within desired accuracies in DFT. We demonstrate using a wide variety of materials systems that SPARC achieves high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; exponential convergence in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consistent and display negligible 'egg-box' effect; accurate properties of crystals, slabs, and wires; and negligible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementations for systems consisting up to thousands of electrons, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for performing DFT simulations of extended systems.

As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of DensityFunctionalTheory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable 'egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.

As a first step to meet the challenge to calculate the electronic structure and total energy of charged states of atoms and molecules adsorbed on ultrathin insulating films supported by a metallic substrate using densityfunctionaltheory (DFT), we have developed a simplified new DFT scheme that only describes the electrostatic interaction of an external charged system with a metal surface. This purely electrostatic interaction is obtained from the assumption that the electron densities of the two fragments (charged system and metal surface) are non-overlapping and by neglecting non-local exchange-correlation effects such as the van der Waals interactions between the two fragments. In addition, the response of the metal surface to the electrostatic potential from the charged system is treated to linear order, whereas the charged system is treated fully within DFT. In particular, we consider the classical perfect conductor model for the metal response, although our formalism is not limited to this approximation. To test the computational implementation of this new scheme, we have considered the case of a Na+ cation interacting with a perfect conductor. The application of this new methodology to realistic problems involving charged systems adsorbed on insulating films supported by a metal surface are deferred to a separate following publication.

The densityfunctionaltheory, simplified by the local density approximation and mean-field approximation, is applied to study the surface properties of pure non-polar fluids. A reasonable long rang correction is adopted to avoid the truncation of the potential. The perturbation theory is applied to establish the equation for the phase equilibrium, in which the hard-core chain fluid is as the reference fluid and the Yukawa potential is used as the perturbation term. Three parameters, elk, d and ms, are regressed from the vapor-liquid equilibria, and the surface properties, including density profile, surface tension and local surface tension profile are predicted with these parameters.

The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of densityfunctionaltheory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few illustrative numerical calculations are shown to predict the molecular polarizabilities in good agreement with available results. The usefulness of the approach to the calculation of intermolecular interaction needed for computer simulation is highlighted.

An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse and relies on a long-range-interacting wave function instead...... expression when expanded in perturbation theory. In contrast to the usual RSDH functionals, RSDHf describes the coupling between long- and short-range correlations as an orbital-dependent contribution. Calculations on the first four noble-gas dimers show that this coupling has a significant effect...

Within the framework of the densityfunctionaltheory for classical fluids,the equilibrium density profiles of charged hard sphere fluid confined in micro-cavity are studied by means of the modified fundamental measure theory.The dimension of micro-cavity,the charge of hard sphere and the applied electric field are found to have significant effects on the density profiles.In particular,it is shown that Coulomb interaction,excluded volume interaction and applied electric Geld play the central role in controlling the aggregated structure of the system.

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent densityfunctionaltheory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.

The Seebeck coefficient plays a fundamental role in identifying the efficiency of a thermoelectric device. Its theoretical evaluation for atomistic models is routinely based on densityfunctionaltheory calculations combined with the Landauer-Büttiker approach to quantum transport. This combination, however, suffers from serious drawbacks for devices in the Coulomb blockade regime. We show how to cure the theory through a simple correction in terms of the temperature derivative of the exchange correlation potential. Our results compare well with both rate equations and experimental findings on carbon nanotubes.

One of the most important open challenges in modern Kohn-Sham (KS) density-functionaltheory (DFT) is the correct treatment of systems involving fractional electron charges and spins. Approximate exchange-correlation functionals struggle with such systems, leading to pervasive delocalization and static correlation errors. We demonstrate how these errors, which plague density-functional calculations of bond-stretching processes, can be avoided by employing the alternative framework of partition density-functionaltheory (PDFT) even using the local density approximation for the fragments. Our method is illustrated with explicit calculations on simple systems exhibiting delocalization and static-correlation errors, stretched H2 (+), H2, He2 (+), Li2 (+), and Li2. In all these cases, our method leads to greatly improved dissociation-energy curves. The effective KS potential corresponding to our self-consistent solutions displays key features around the bond midpoint; these are known to be present in the exact KS potential, but are absent from most approximate KS potentials and are essential for the correct description of electron dynamics.

We use coupled-cluster quantum chemical methods to calculate the energetics of molecular clusters cut out of periodic molecular hydrogen structures that model observed phases of solid hydrogen. The hydrogen structures are obtained from Kohn-Sham densityfunctionaltheory (DFT) calculations at pressures of 150, 250 and 350 GPa, which are within the pressure range in which phases II, III and IV are found to be stable. The calculated deviations in the DFT energies from the coupled-cluster data are reported for different functionals, and optimized functionals are generated which provide reduced errors. We give recommendations for semi-local and hybrid densityfunctionals that are expected to accurately describe hydrogen at high pressures.

We use coupled-cluster quantum chemical methods to calculate the energetics of molecular clusters cut out of periodic molecular hydrogen structures that model observed phases of solid hydrogen. The hydrogen structures are obtained from Kohn-Sham densityfunctionaltheory (DFT) calculations at pressures of 150, 250, and 350 GPa, which are within the pressure range in which phases II, III, and IV are found to be stable. The calculated deviations in the DFT energies from the coupled-cluster data are reported for different functionals, and optimized functionals are generated which provide reduced errors. We give recommendations for semilocal and hybrid densityfunctionals that are expected to provide an accurate description of hydrogen at high pressures.

A novel nonempirical scaling correction method is developed to tackle the challenge of band gap prediction in densityfunctionaltheory. For finite systems the scaling correction largely restores the straight-line behavior of electronic energy at fractional electron numbers. The scaling correction can be generally applied to a variety of mainstream densityfunctional approximations, leading to significant improvement in the band gap prediction. In particular, the scaled version of a modified local density approximation predicts band gaps with an accuracy consistent for systems of all sizes, ranging from atoms and molecules to solids. The scaled modified local density approximation thus provides a useful tool to quantitatively characterize the size-dependent effect on the energy gaps of nanostructures.

Prof. Walter Kohn presents "Electronic structure of matter : wave functions and densityfunctionals".Since the 1920's Schroedinger wave functions have been the principal theoretical concept for understanding and computing the electronic structure of matter. More recently, DensityFunctionalTheory (DFT), couched in terms of the electronic density distribution, n(r), has provided a new perspective and new computational possibilities, especially for systems consisting of very many (up to ~1000) atoms. In this talk some fundamental limitations of wave function methods for very-many-atom-systems will be discussed. The DFT approach will be explained together with some physical/chemical applications and a discussion of its strenghts and weaknesses. W Kohn has received the prize with J A Pople for his development of computational methods in quantum chemistr.

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as densityfunctionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing densityfunctionals for use in quantum algorithms.

We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear densityfunctionaltheory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy densityfunctional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and charge-independence-breaking studies offered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.

Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent densityfunctionaltheory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and densityfunctional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.

Excited state surfaces in densityfunctionaltheory and the problem of charge transfer are considered from an orbital overlap perspective. For common densityfunctional approximations, the accuracy of the surface will not be uniform if the spatial overlap between the occupied and virtual orbitals involved in the excitation has a strong conformational dependence; the excited state surface will collapse toward the ground state in regions where the overlap is very low. This characteristic is used to predict and to provide insight into the breakdown of excited state surfaces in the classic push-pull 4-(dimethylamino)benzonitrile molecule, as a function of twist angle. The breakdown is eliminated using a Coulomb-attenuated functional. Analogous situations will arise in many molecules.

We assess the accuracy of eight Minnesota densityfunctionals (M05 through M08-SO) and two others (PBE and PBE0) for the prediction of electronic excitation energies of a family of four cyanine dyes. We find that time-dependent densityfunctionaltheory (TDDFT) with the five most recent of these functionals (from M06-HF through M08-SO) is able to predict excitation energies for cyanine dyes within 0.10-0.36 eV accuracy with respect to the most accurate available Quantum Monte Carlo calculations, providing a comparable accuracy to the latest generation of CASPT2 calculations, which have errors of 0.16-0.34 eV. Therefore previous conclusions that TDDFT cannot treat cyanine dyes reasonably accurately must be revised.

through first principle methods. Ensembles generated using a Bayesian error estimation functional, in this case the BEEF-vdW functional[6], are used for the error identification. The ensembles, which consist of perturbations of the main van der Waals densityfunctional, can be generated at low......Densityfunctionaltheory (DFT) calculations have greatly contributed to the atomic level understanding of electrochemical reactions. However, in some cases, the accuracy can be prohibitively low for a detailed understanding of, e.g. reaction mechanisms. Two cases are examined here, i...... that the systematic error is due to carbon-oxygen double bonds, as the change in number of carbon-oxygen double bonds in the reaction to methanol is two as compared to one for reaction to formic acid. This is subsequently confirmed by further comparisons of functional dependence and a significant source of systematic...

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to extrapolate beyond the regions reached by experiment; and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear densityfunctionaltheory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy densityfunctional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, w...

Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a densityfunctionaltheory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.

We develop a general densityfunctionaltheory for polyatomic molecules by taking the complete association limit of Wertheim's thermodynamic perturbation theory in a general way. By enforcing the complete association limit at an early point in the derivation and introducing the concept of molecular graphs, a general form for the free energy functional and segment densities are developed for both rigid and semiflexible molecules. The theory is applicable to branched chains, rings, or any other molecular structure. As an example the theory is applied as a second order perturbation theory to the case of molecules with a rigid three segment head and a fully flexible tail in a slit pore where bond angle of the rigid portion is an independent variable.

It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.

Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical densityfunctionaltheory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical densityfunctional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical densityfunctionaltheory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid

Classical densityfunctionaltheory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Non-perturbative study of "real-time" field theories is difficult due to the sign problem. We use Bold Schwinger-Dyson (SD) equations to study the real-time $\\phi^4$ theory in $d=4$ beyond the perturbative regime. Combining SD equations in a particular way, we derive a non-linear integral equation for the two-point function. Then we introduce a new method by which one can analytically perform the momentum part of loop integrals in this equation. The price we must pay for such simplification is to numerically solve a non-linear integral equation for the spectral densityfunction. Using Bold diagrammatic Monte Carlo method we find non-perturbative spectral function of theory and compare it with the one obtained from perturbation theory. At the end we utilize our Monte Carlo result to find the full vertex function as the basis for the computation of real-time scattering amplitudes.

To speak about fundamental measure theory obliges us to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only densityfunctionaltheory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three dimensional) with that of squares (two dimensional) and rods (one dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered-cubic, and body-centered-cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.

Quantitative, predictive theories for metal--electrolyte interfaces require an atomic-scale representation of the interface, which must include an accurate statistical description of a polar fluid in contact with a solid surface; and also a description of the electronic density and structure of a metal surface in contact with a fluid. Such a complex system presents a difficult computational problem, and has been dealt with in the past essentially by parts; either by molecular dynamics calculations of the fluid structure, or densityfunctional calculations of the metal--surface electronic structure. A complete and self-consistent determination of the surface structure would, however, involve a simultaneous calculation of both the atomic and electronic structure of the interface. This suggests a combination of these two calculational techniques, and it is just this sort of molecular dynamics and densityfunctional combination which comprises the Car--Parrinello, and related, methods. We have developed a Car--Parrinello type combination of molecular dynamics and densityfunctional methods, suitable for application to the metal--electrolyte interface. We briefly describe this calculation and discuss our initial results for a fairly simple metal--water interface.

We investigate fractional-charge and fractional-spin errors in range-separated density-functionaltheory. Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation densityfunctional, and the RSH+MP2 method which adds long-range second-order M{{\\o}}ller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corre...

The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator □ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment (˜MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.

A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) densityfunctiontheory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free densityfunctionaltheory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent densityfunctionaltheory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.

Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on densityfunctionaltheory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission.

Using time-evolution time-dependent densityfunctionaltheory (TDDFT) within the adiabatic local-density approximation, we study the interactions between single electrons and molecular resonances at surfaces. Our system is a nitrogen molecule adsorbed on a ruthenium surface. The surface is modeled...... resonance and the lowering of the resonance energy due to an image charge effect. Finally we apply the TDDFT procedure to only consider the decay of molecular excitations and find that it agrees quite well with the width of the projected density of Kohn-Sham states....

It is now possible to compute IR (infrared) spectra of large molecules with an accuracy of 30 per cm, or better, using densityfunctiontheory. This is true for cations, anions, and neutrals. Thus it possible to generate synthetic IR spectra that can help interpret experimental spectra and fill in for missing experimental data. These synthetic spectra can be used as input into interstellar models. In addition to IR spectra, it is possible to compute energetic properties to help understand which molecules can be formed in the interstellar environment.

Effect of solvation on coumarin6 dye has been studied with densityfunctionaltheory (DFT). Optimized structure of the dye has been obtained in various solvents and frequencies of various vibrational bands have been calculated in these solvents. Calculations predict shift in the frequency of certain bands in the solvents. Similar shifts have been observed experimentally in the vibrational spectra of the dye in solvents. In order to ascertain the origin of these shifts, the interactions of solvent molecules with the coumarin6 molecule have been studied using various tools of DFT like donor-acceptor interactions, Molecular Electrostatic potential (MEP) and HOMO-LUMO analysis etc.

We present a method to make highly accurate pseudopotentials for use with orbital-free densityfunctionaltheory (OF-DFT) with given exchange-correlation and kinetic energy functionals, which avoids the compounding of errors of Kohn-Sham DFT and OF-DFT. The pseudopotentials are fitted to reference (experimental or highly accurate quantum chemistry) values of interaction energies, geometries, and mechanical properties, using a genetic algorithm. This can enable routine large-scale ab initio simulations of many practically relevant materials. Pseudopotentials for Li, Na, and Mg resulting in accurate geometries and energies of different phases as well as of vacancy formation and bulk moduli are presented as examples.

The combination of genetic algorithm and neural network approach (GANN) has been developed to improve the calculation accuracy of densityfunctionaltheory. As a demonstration, this combined quantum mechanical calculation and GANN correction approach has been applied to evaluate the optical absorption energies of 150 organic molecules. The neural network approach reduces the root-mean-square (rms) deviation of the calculated absorption energies of 150 organic molecules from 0.47 to 0.22 eV for the TDDFTB3LYP6-31G(d) calculation, and the newly developed GANN correction approach reduces the rms deviation to 0.16 eV.

inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functionaltheory-MC-srDFT-as a new tool in the toolbox. While initial applications for systems with multireference character......-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2...

We investigate the molecular structure and vibrational properties of perchlorinated hexa-peri-hexabenzocoronene (HBC-Cl) by densityfunctionaltheory (DFT) calculations and IR and Raman spectroscopy, in comparison to the parent HBC. The theoretical and experimental IR and Raman spectra demonstrated very good agreement, elucidating a number of vibrational modes corresponding to the observed peaks. Compared with the parent HBC, the edge chlorination significantly alters the planarity of the molecule. Nevertheless, the results indicated that such structural distortion does not significantly impair the π-conjugation of such polycyclic aromatic hydrocarbons.

The core structures of (I 11) screw dislocations in bee metals are studied using densityfunctionaltheory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180degrees rotations around an axis perpendicular...... to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of gamma surfaces and the elastic constants B, C' and c(44) are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point...

First principle calculations of the electronic structure and magnetic interaction of GaN:Gd have been performed within the Generalized Gradient Approximation (GGA) of the densityfunctionaltheory (DFT) with the on-site Coulomb energy U taken into account (also referred to as GGA+U). The ferromagnetic p-d coupling is found to be over two orders of magnitude larger than the s-d exchange coupling. The experimental colossal magnetic moments and room temperature ferromagnetism in GaN:Gd reported recently are explained by the interaction of Gd 4f spins via p-d coupling involving holes introduced by intrinsic defects such as Ga vacancies.

The band structure of Cu(2)O is calculated using densityfunctionaltheory in the generalized gradient approximation. By taking spin-orbit coupling into account the split between the Γ(7)(+) and the Γ(8)(+) valence band states is obtained as 128 meV. The highest valence band shows a noticeable nonparabolicity close to the Γ point. This is important for the quantitative description of excitons in this material, which is considered to be the best candidate for the confirmation that Bose-Einstein condensation also occurs in excitonic systems.

Electronic and structural analysis of buckled antimonene has been performed using densityfunctionaltheory-based ab-initio approach. Geometrical parameters such as bond length and bond angle are very close to the single ruffle layer of rhombohedral antimony. Phonon dispersion along the high symmetry point of the Brillouin zone does not signify any soft mode. Electronic indirect band gap of 1.61 eV is observed for the single-layer antimonene. However, the occurrence of bilayered quasi-2D sheet consequent to metallic behaviour is due to significant electronic charge dispersion between interlayer region.

We derive an exchange energy functional of generalized gradient form with a corresponding potential that changes discontinuously at integer particle numbers. The functional is semilocal, yet incorporates key features that are connected to the derivative discontinuity of Kohn-Sham density-functionaltheory. We validate our construction for several paradigm systems and explain how it addresses central well-known deficiencies of antecedent semilocal methods, i.e., the description of charge transfer, properly localized orbitals, and band gaps. We find, e.g., an improved shell structure for atoms, eigenvalues that more closely correspond to ionization energies, and an improved description of band structure where localized states are lowered in energy.

A MinMax self-consistent-field (SCF) approach is derived in the framework of auxiliary densityfunctionaltheory. It is shown that the SCF convergence can be guided by the fitting coefficients that arise from the variational fitting of the Coulomb potential. An in-core direct inversion of the iterative subspace (DIIS) algorithm is presented. Due to its reduced memory demand this new in-core DIIS method can be applied without overhead to very large systems with tens of thousands of basis and auxiliary functions. Due to the new DIIS error definition systems with fractional occupation numbers can be treated, too.

A density-functionaltheory study of the electrochemical adsorption of sulfuric acid anions was conducted at the Pt(111)/electrolyte interface over a wide range of electrode potential, including the anomalous region of the hydrogen voltammogram of this electrode. We focus on the precise nature of the binding species and their bonding to the surface, identifying the adsorbed species as a function of electrode potential. In particular, the origin of anomalous or so-called "butterfly" feature in this voltammogram between +0.30 and +0.50 V vs. the reference hydrogen electrode and the nature of the adsorbed species on the Pt(111) surface in this potential range were explicated.

Electronic and structural analysis of buckled antimonene has been performed using densityfunctionaltheory-based $\\it{ab-initio}$ approach. Geometrical parameters such as bond length and bond angle are very close to the single ruffle layer of rhombohedral antimony. Phonon dispersion along the high symmetry point of the Brillouin zone does not signify any soft mode. Electronic indirect band gap of 1.61 eV is observed for the single-layer antimonene. However, the occurrence of bilayered quasi-2D sheet consequent to metallic behaviour is due to significant electronic charge dispersion between interlayer region.

Molybdenum oxide (MoO3) is an important material that is being considered for numerous technological applications, including catalysis and electrochromism. In the present study, we apply hybrid densityfunctionaltheory to investigate O and Mo vacancies in the orthorhombic phase. We determine the vacancy formation energies of different defect sites as functions of the electron chemical potential, addressing different charge states. In addition, we investigate the consequences of defects for the material properties. Ultraviolet photoemission spectroscopy is employed to study the valence band of stoichiometric and O defective MoO3. We show that O vacancies result in occupied in-gap states.

The Bethe-Salpeter equation (BSE) accurately describes the optical properties of solids, but is computationally expensive. Time-dependent density-functionaltheory (TDDFT) is more efficient, but standard functionals do not produce excitons in extended systems. We present a new, non-empirical hybrid TDDFT approach whose computational cost is much less than BSE, while the accuracy for both bound excitons and the continuum spectra is comparable to that of the BSE. Good performance is observed for both small-gap semiconductors and large-gap insulators. Work supported by NSF Grant DMR-1408904.

Time-dependent density-functionaltheory (TDDFT) is an efficient method to describe the optical properties of solids. Lately, a series of bootstrap-type exchange-correlation (xc) kernels have been reported to produce accurate excitons in solids, but different bootstrap-type kernels exist in the literature, with mixed results. In this presentation, we reveal the origin of the confusion and show a new empirical TDDFT xc kernel to compute excitonic properties of semiconductors and insulators efficiently and accurately. Our method can be used for high-throughput screening calculations and large unit cell calculations. Work supported by NSF Grant DMR-1408904.

The computational bottleneck for performing path-integral molecular dynamics (PIMD) for nuclei on a first principles electronic potential energy surface has been the speed with which forces from the electrons can be generated. Recent advances in orbital-free densityfunctionaltheory (OF-DFT) not only allow for faster generation of first principles forces but also include the effects of temperature on the electron density. We will present results of calculations on hydrogen in warm dense matter conditions where the protons are described by PIMD and the electrons by OF-DFT. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.

Electronic and magnetic properties of Pd-Ni multilayers have been studied using VASP method in the framework of the densityfunctionaltheory (DFT). The calculations performed for different configurations (Pd n/Ni m(1 1 1), where n Pd layers are piled up over m Ni layers with n=0 to 4 and n+m=4), reveal that the important magnetic moment of Ni is significantly enhanced according as n increases due to hybridization effects between Pd and Ni mostly localized at the interface. The results also indicate that the Pd atoms are strongly polarized in the studied systems when compared with the pure metal.

Electronic and magnetic properties of Pd-Ni multilayers have been studied using VASP method in the framework of the densityfunctionaltheory (DFT). The calculations performed for different configurations (Pd{sub n}/Ni{sub m}(1 1 1), where n Pd layers are piled up over m Ni layers with n=0 to 4 and n+m=4), reveal that the important magnetic moment of Ni is significantly enhanced according as n increases due to hybridization effects between Pd and Ni mostly localized at the interface. The results also indicate that the Pd atoms are strongly polarized in the studied systems when compared with the pure metal.

The measurement of the lattice-parameter of silicon by x-ray interferometry assumes the use of strain-free crystals. This might not be the case because surface relaxation, reconstruction, and oxidation cause strains without the application of any external force. In a previous work, this intrinsic strain was estimated by a finite element analysis, where the surface stress was modeled by an elastic membrane having a 1 N/m tensile strength. The present paper quantities the surface stress by a densityfunctionaltheory calculation. We found a value exceeding the nominal value used, which potentially affects the measurement accuracy.

Electronic structure calculations employing screened hybrid densityfunctionaltheory are used to gain fundamental insight into the interaction of carbon interstitial (Ci) and substitutional (Cs) atoms forming the CiCs defect known as G-center in silicon (Si). The G-center is one of the most important radiation related defects in Czochralski grown Si. We systematically investigate the density of states and formation energy for different types of CiCs defects with respect to the Fermi energy for all possible charge states. Prevalence of the neutral state for the C-type defect is established.

Densityfunctionaltheory calculations can be used to gain valuable insight into the fundamental reaction processes in metal−oxygen systems, e.g., metal−oxygen batteries. Here, the ability of a range of different exchange-correlation functionals to reproduce experimental enthalpies of formation...... for different types of alkali and alkaline earth metal oxide species has been examined. Most examined functionals result in significant overestimation of the stability of superoxide species compared to peroxides and monoxides, which can result in erroneous prediction of reaction pathways. We show that if metal...

Densityfunctionaltheory calculations have been performed for the three elementary steps―Tafel, Heyrovsky, and Volmer―involved in the hydrogen oxidation reaction (HOR) and its reverse, the hydrogen evolution reaction (HER). For the Pt(111) surface a detailed model consisting of a negatively...... charged Pt(111) slab and solvated protons in up to three water bilayers is considered and reaction energies and activation barriers are determined by using a newly developed computational scheme where the potential can be kept constant during a charge transfer reaction. We determine the rate limiting...

In these proceedings, we show that time-dependent densityfunctionaltheory is capable of stopping calculations at the extreme conditions of temperature and pressure seen in warm dense matter. The accuracy of the stopping curves tends to be up to about 20% lower than empirical models that are in use. However, TDDFT calculations are free from fitting parameters and assumptions about the model form of the dielectric function. This work allows the simulation of ion stopping in many materials that are difficult to study experimentally. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

In this short paper, the authors report a new computational approach in the context of DensityFunctionalTheory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap matrices and solving the associated generalized eigenproblems $Ax = \\lambda Bx$ constitute the two most time-consuming fractions of each iteration. Two promising directions, implementing the new methodology, are presented that will ultimately improve the performance of the generalized eigensolver and save computational time.

WO3 bulk and various surfaces are studied by an ab-initio densityfunctionaltheory technique.The band structures and electronic density states of WO3 bulk are investigated.The surface energies of different WO3 surfaces are compared and then the(002)surface with minimum energy is computed for its NH3 sensing mechanism which explains the results in the experiments.Three adsorption sites are considered.According to the comparisons of the energy and the charge change between before and after adsorption in the optimal adsorption site O1c,the NH3 sensing mechanism is obtained.

The interaction of atomic hydrogen with two linear polycyclic aromatic hydrocarbons (PAHs), anthracene and polyacene (the polymer of benzene), was studied within the densityfunctionaltheory (DFT). Using a proper dispersion-corrected method (DFT-D) the preferential physisorption sites were explored. The activation barrier for the bond formation between a peripheral C and the incoming H was calculated to be 58.5 and 34.1 meV with pure DFT on anthracene and polyacene at its antiferromagnetic ground state, respectively. DFT-D, although improves the description of the physisorbed state, tends to underestimate the chemisorption barriers due an artifact arising from the dispersion correction.

Full Text Available Theoretical reactivity indices based on the conceptual DensityFunctionalTheory (DFT have become a powerful tool for the semiquantitative study of organic reactivity. A large number of reactivity indices have been proposed in the literature. Herein, global quantities like the electronic chemical potential μ, the electrophilicity ω and the nucleophilicity N indices, and local condensed indices like the electrophilic P k + and nucleophilic P k − Parr functions, as the most relevant indices for the study of organic reactivity, are discussed.

All methionine aminopeptidases exhibit the same conserved metal binding site. The structure of this site with either Co2+ ions or Zn2+ ions was investigated using densityfunctionaltheory. The calculations showed that the structure of the site was not influenced by the identity of the metal ions...... oxygen, which is part of either a water molecule or a hydroxide ion. Within the site of hMetAP-2 the results strongly indicate that a hydroxide ion bridges the metal ions. By contrast, the nature of the oxygen bridging the metal ions within the metal binding site of eMetAP-1 cannot be determined based...

It is now possible to compute IR (infrared) spectra of large molecules with an accuracy of 30 per cm, or better, using densityfunctiontheory. This is true for cations, anions, and neutrals. Thus it possible to generate synthetic IR spectra that can help interpret experimental spectra and fill in for missing experimental data. These synthetic spectra can be used as input into interstellar models. In addition to IR spectra, it is possible to compute energetic properties to help understand which molecules can be formed in the interstellar environment.

Densityfunctionaltheory employing hybrid functional is used to gain fundamental insight into the interaction of vacancies with oxygen interstitials to form defects known as A-centers in silicon. We calculate the formation energy of the defect with respect to the Fermi energy for all possible charge states. It is found that the neutral and doubly negatively charged A-centers dominate. The findings are analyzed in terms of the density of states and discussed in view of previous experimental and theoretical studies.

A densityfunctionaltheory for a mixture of hard rods and polymers modeled as chains built of hard tangent spheres is proposed by combining the functional due to Yu and Wu for the polymer mixtures [J. Chem. Phys. 117, 2368 (2002)] with Schmidt's functional [Phys. Rev. E 63, 50 201 (2001)] for rod-sphere mixtures. As a simple application of the functional, the demixing transition into polymer-rich and rod-rich phases is examined. When the chain length increases, the phase boundary broadens and the critical packing fraction decreases. The shift of the critical point of a demixing transition is most noticeable for short chains.

An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] and relies on a long-range interacting wavefunction instead of the non-interacting Kohn-Sham one. When second-order corrections to the density are neglected, the energy expression reduces to a range-separated double-hyb...

We discuss the applicability of long-range separated densityfunctionaltheory (DFT) to the prediction of electronic transitions of a particular photocatalytic system based on an Ir(III) photosensitizer (IrPS). Special attention is paid to the charge-transfer properties which are of key importance for the photoexcitation dynamics, but and cannot be correctly described by means of conventional DFT. The optimization of the range-separation parameter is discussed for IrPS including its complexes with electron donors and acceptors used in photocatalysis. Particular attention is paid to the problems arising for a description of medium effects by a polarizable continuum model.

We investigate the equilibrium of a fluid in contact with a solid boundary through a density-functionaltheory. Depending on the conditions, the fluid can be in one phase, gas or liquid, or two phases, while the wall induces an external field acting on the fluid particles. We first examine the case of a liquid film in contact with the wall. We construct bifurcation diagrams for the film thickness as a function of the chemical potential. At a specific value of the chemical potential, two equal...

The experiments of carvedilol form II, form III, and hydrate by (13)C and (15)N cross-polarization magic-angle spinning (CP MAS) are reported. The GIPAW (gauge-including projector-augmented wave) method from DFT (densityfunctionaltheory) calculations was used to simulate (13)C and (15)N chemical shifts. A very good agreement was found for the comparison between the global results of experimental and calculated nuclear magnetic resonance (NMR) chemical shifts for carvedilol polymorphs. This work aims a comprehensive understanding of carvedilol crystalline forms employing solution and solid-state NMR as well as DFT calculations.

We develop a multicomponent hydrodynamic model based on moments of the Born-Bogolyubov-Green-Kirkwood-Yvon hierarchy equations for physical conditions relevant to astrophysical plasmas. These equations incorporate strong correlations through a densityfunctionaltheory closure, while transport enters through a relaxation approximation. This approach enables the introduction of Coulomb coupling correction terms into the standard Burgers equations. The diffusive currents for these strongly coupled plasmas is self-consistently derived. The settling of impurities and its impact on cooling can be greatly affected by strong Coulomb coupling, which we show can be quantified using the direct correlation function.

We use the classical version of the density-functionaltheory in the weighted-density approximation to build up the entire phase diagram and the interface structure of a two-dimensional lattice-gas model which is known, from previous studies, to possess three stable phases -- solid, liquid, and vapour. Following the common practice, the attractive part of the potential is treated in a mean-field-like fashion, although with different prescriptions for the solid and the fluid phases. It turns o...

A densityfunctionaltheory (DFT)-based, combinatorial search for improved oxygen reduction reaction (ORR) catalysts is presented. A descriptor-based approach to estimate the ORR activity of binary surface alloys, wherein alloying occurs only in the surface layer, is described, and rigorous......, potential-dependent computational tests of the stability of these alloys in aqueous, acidic environments are presented. These activity and stability criteria are applied to a database of DFT calculations on nearly 750 binary transition metal surface alloys; of these, many are predicted to be active...

Densityfunctionaltheory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.

The formation of VO (A-center), VV and VO2 defects in irradiated Czochralski-grown silicon (Si) is of technological importance. Recent theoretical studies have examined the formation and charge states of the A-center in detail. Here we use densityfunctionaltheory employing hybrid functionals to analyze the formation of VV and VO2 defects. The formation energy as a function of the Fermi energy is calculated for all possible charge states. For the VV and VO2 defects double negatively charged and neutral states dominate, respectively.

@@ We employ a real-space pseudopotential method to determine the ground state structure of the carbon cluster C6 via simulated annealing and the corresponding optical absorption spectra from the adiabatic time-dependent density-functionaltheory (TDDFT) and the local density approximation (TDLDA). It is found that the ground state structure of the carbon cluster C6 belongs to a monocyclic D3h structure and the calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.

The molecular structure and vibrational spectra of ciprofloxacin(1-cyclopropyl-6-fluoro-1,4-dihydro-4-oxo-7-(1-piperazinyl)-3-quinolinecarboxylic acid) have been calculated using the different densityfunctionaltheory (DFT) methods and various basis sets. This paper examines the comparative performance of different DFT methods at various basis sets in predicting molecular and vibrational spectra of ciprofloxacin. The calculation results show that SVWN/LANL2DZ level and SVWN/6-31G level offer the highest certainty to predict the structure and vibrational spectra of ciprofloxacin, respectively.

We show that the type 2 Broyden secant method is a robust general purpose mixer for self consistent field problems in densityfunctionaltheory. The Broyden method gives reliable convergence for a large class of problems and parameter choices. We directly mix the approximation of the electronic density to provide a basis independent mixing scheme. In particular, we show that a single set of parameters can be chosen that give good results for a large range of problems. We also introduce a spin transformation to simplify treatment of spin polarized problems. The spin transformation allows us to treat these systems with the same formalism as regular fixed point iterations.

Urea L-malic acid, a new second order nonlinear optical crystal, was studied using densityfunctionaltheory (DFT). PBEPBE/6-31+G(d,p) method, the optimal method for comparing the results from thc sevcral DFT methods, was chosen to study the molecular structure. Infrared and ultraviolet-visible spectra were obtained and compared with experiments. The ultraviolet-visible spectrum was also analyzed by the molecular orbital population. The geometries, and the infrared and ultraviolet-visible spectra in water were studied using DFT methods in combination with the polarized continuum model to predict the perturbations by the solvent effect.

Full Text Available Densityfunctionaltheory has been employed to investigate the deformation behaviors of glassy Fe-Si-B model systems prepared by ab initio molecular dynamics. The atomistic deformation defects which are closely related to the local dilation volumes or excess volumes and unstable bonding have been systematically analyzed. It has been found that the icosahedral structures are relatively stable under shear deformation until fracture occurs. Plastic flow is indicated by interruption of percolating icosahedral structures, caused by unstable Fe-Si bonding of p-s hybridization in nature.

Multi-configuration range-separated density-functionaltheory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range Multi-Configuration- Self-Consistent Field (MCSCF) treatment with an adiabatic short...... in Be and the 11u+ state in the stretched H molecule are improved, although the latter is still significantly underestimated. Exploratory TD-MC-srDFT/GGA calculations for ferrocene yield in general excitation energies at least as good as TD-DFT using the Coulomb attenuated method based on the three-parameter Becke...

In this work, the nuclear reactivity indices of densityfunctionaltheory have been generalized to the spin polarized case and their relationship to electron spin polarized indices has been established. In particular, the spin polarized version of the nuclear Fukui function has been proposed and a finite difference approximation has been used to evaluate it. Applications to a series of triatomic molecules demonstrate the ability of the new functions to predict the geometrical changes due to a change in the spin multiplicity. The main equations in the different ensembles have also been presented.

We present a generalization of DensityFunctionalTheory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent densityfunctionaltheory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

Two different adsorption configurations of benzene on the Si(001)-(2×1) surface, the tight-bridge and butterfly structures, were studied using densityfunctionaltheory. Several exchange and correlation functionals were used, including the recently developed van der Waals densityfunctional (vdW-...

We present an extension of our recently introduced molecular densityfunctionaltheory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619, 2013] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields, the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional ...

Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic densityfunctionaltheory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.

Full Text Available Hard spheres are a central and important model reference system for both homogeneous and inhomogeneous fluid systems. In this paper we present new high-precision molecular-dynamics computer simulations for a hard sphere fluid at a planar hard wall. For this system we present benchmark data for the density profile ρ(z at various bulk densities, the wall surface free energy γ, the excess adsorption Γ, and the excess volume v_{ex}, which is closely related to Γ. We compare all benchmark quantities with predictions from state-of-the-art classical densityfunctionaltheory calculations within the framework of fundamental measure theory. While we find overall good agreement between computer simulations and theory, significant deviations appear at sufficiently high bulk densities.

We apply the adiabatic time-dependent densityfunctionaltheory to magnetic ci the real-space, real-time computational method. The standard formulas for the MCD response and its A and B terms are derived from the observables in the time-dependent wave function. We find the real time method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCD sum rules are derived and interpreted in the real-time formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C-60 using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the A and B terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.

Motivated by recent observational data, the equations of state with the inclusion of strangeness-bearing $\\Lambda$-hyperons and the corresponding properties of neutron stars are studied, based on the covariant densityfunctional (CDF) theory. To this end, we specifically employ the density dependent relativistic Hartree-Fock (DDRHF) theory and the relativistic mean field theory (RMF). The inclusion of $\\Lambda$-hyperons in neutron stars shows substantial effects in softening the equation of state. Because of the extra suppression effect originated from the Fock channel, large reductions on both the star mass and radius are predicted by the DDRHF calculations. It is also found that the mass-radius relations of neutron stars with $\\Lambda$-hyperons determined by DDRHF with the PKA1 parameter set are in fairly good agreement with the observational data where a relatively small neutron stars radius is required. Therefore, it is expected that the exotic degrees of freedom such as the strangeness-bearing structure ...

Insights from molecular simulation have influenced both experiment and theory regarding the understanding of the specific ion effect. Although there seems to be a consensus that large polarizable anions exist at the air-water interface, the understanding of the precise molecular interactions that give rise to surface adsorption remain elusive. I will present our work on the adsorption of iodide at the air-water interface using densityfunctionaltheory (DFT) based interaction potentials. I will discuss similarities and differences of the results obtained using different descriptions of molecular interaction. Last, we are able to reconcile the results obtained with molecular simulation using standard empirical potentials with the dielectric continuum theory of Levin and co-workers.[4pt] In collaboration with Marcel Baer, Pacific Northwest National Laboratory; Douglas Tobias, Abe Stern, University of California, Irvine, CA; and Yan Levin, Instituto de F'isica, UFRGS, Porto Alegre, RS, 91501-970, Brazil.

Densityfunctionaltheory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate densityfunctionaltheory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate densityfunctionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.

Densityfunctionaltheory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate densityfunctionaltheory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate densityfunctionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.

We find an exact analytical solution to the exchange-only time-dependent density-functionaltheory (TDDFT) problem for a significant class of quasi-low-dimensional (QLD) materials: QLD electron gas with only one band filled in the direction perpendicular to the layer or wire. The theory yields the TD exchange potential as an explicit nonlocal operator of the TD spin density. The dressed interband (image states) excitation spectra of quasi-two-dimensional electron gas are obtained, while the comparison with the Kohn-Sham transitions provides insights into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree f_{H} and the exchange f_{x} kernels of TDDFT are found in the low-density regime, elucidating the interrelations between the Kohn-Sham and the many-body dynamics in mesoscopic systems.

We find an exact analytical solution to the exchange-only time-dependent density-functionaltheory (TDDFT) problem for a significant class of quasi-low-dimensional (QLD) materials: QLD electron gas with only one band filled in the direction perpendicular to the layer or wire. The theory yields the TD exchange potential as an explicit nonlocal operator of the TD spin density. The dressed interband (image states) excitation spectra of quasi-two-dimensional electron gas are obtained, while the comparison with the Kohn-Sham transitions provides insights into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree fH and the exchange fx kernels of TDDFT are found in the low-density regime, elucidating the interrelations between the Kohn-Sham and the many-body dynamics in mesoscopic systems.

Full Text Available The weighted densityfunctionaltheory proposed by Tarazona is applied to study the solid-liquid interface. In the last two decades the weighted densityfunctional became a useful tool to consider the properties of inhomogeneous liquids. In this theory, the role of the size of molecules or the particles of which the matter is composed, was found to be important. In this resarch we study a hard sphere fluid beside a hard wall. For this study the liquid is an inhomogeneous system. We use the definition of the direct correlation function as a second derivative of free energy with respect to the density. We use this definition and the definition of the weighting function, then we minimize the grand potential with respect to the density to get the Euler Lagrange equation and we obtain an integral equation to find the inhomogeneous density profile. The obtained density profile as a function of the distance from the wall, for different bulk density is plotted in three dimensions. We also calculate the pressure and compare it with the Carnahan-starling results, and finally we obtained the surface tension at liquid-solid interface and compared it with the results of Monte Carlo simulation.

The large intrinsic bandgap of NiO hinders its potential application as a photocatalyst under visible-light irradiation. In this study, we have performed first-principles screened exchange hybrid densityfunctionaltheory with the HSE06 functional calculations of N- and C-doped NiO to investigate the effect of doping on the electronic structure of NiO. C-doping at an oxygen site induces gap states due to the dopant, the positions of which suggest that the top of the valence band is made up primarily of C 2p-derived states with some Ni 3d contributions, and the lowest-energy empty state is in the middle of the gap. This leads to an effective bandgap of 1.7 eV, which is of potential interest for photocatalytic applications. N-doping induces comparatively little dopant-Ni 3d interactions, but results in similar positions of dopant-induced states, i.e., the top of the valence band is made up of dopant 2p states and the lowest unoccupied state is the empty gap state derived from the dopant, leading to bandgap narrowing. With the hybrid densityfunctionaltheory (DFT) results available, we discuss issues with the DFT corrected for on-site Coulomb description of these systems.

Different models for aluminum oxynitride (AlON) were calculated using densityfunctionaltheory and optimized using an evolutionary algorithm. Evolutionary algorithm and densityfunctionaltheory (DFT) calculations starting from several models of AlON with different Al or O vacancy locations and different positions for the N atoms relative to the vacancy were carried out. The results show that the constant anion model [McCauley et al., J. Eur. Ceram. Soc. 29(2), 223 (2009)] with a random distribution of N atoms not adjacent to the Al vacancy has the lowest energy configuration. The lowest energy structure is in a reasonable agreement with experimental X-ray diffraction spectra. The optimized structure of a 55 atom unit cell was used to construct 220 and 440 atom models for simulation cells using DFT with a Gaussian basis set. Cubic elastic constant predictions were found to approach the experimentally determined AlON single crystal elastic constants as the model size increased from 55 to 440 atoms. The pressure dependence of the elastic constants found from simulated stress-strain relations were in overall agreement with experimental measurements of polycrystalline and single crystal AlON. Calculated IR intensity and Raman spectra are compared with available experimental data.

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling densityfunctionaltheory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling densityfunctionaltheory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.

The application of first-principles calculations holds promise for greatly improving our understanding of semiconductor superlattices. Developing a procedure to accurately predict band gaps using hybrid densityfunctionaltheory lays the groundwork for future studies investigating more nuanced properties of these structures. Our approach allows a priori prediction of the properties of SLS structures using only the band gaps of the constituent materials. Furthermore, it should enable direct investigation of the effects of interface structure, e.g., intermixing or ordering at the interface, on SLS properties. In this paper, we present band gap data for various InAs/GaSb type-II superlattice structures calculated using the generalized Kohn-Sham formulation of densityfunctionaltheory. A PBE0-type hybrid functional was used, and the portion of the exact exchange was tuned to fit the band gaps of the binary compounds InAs and GaSb with the best agreement to bulk experimental values obtained with 18% of the exact exchange. The heterostructures considered in this study are 6 monolayer (ML) InAs/6 ML GaSb, 8 ML InAs/8 ML GaSb and 10 ML InAs/10 ML GaSb with deviations from the experimental band gaps ranging from 3% to 11%.

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear densityfunctionaltheory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy densityfunctional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. As a result, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

The exchange-correlation energy in Kohn-Sham densityfunctionaltheory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of densityfunctionaltheory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

Full Text Available The relationship between microstructure and hydrogenation properties of the mixed metals has been investigated via different spectroscopic techniques and the densityfunctionaltheory (DFT. FESEM and TEM analyses demonstrated the nano-grains of Mg2NiH4 and MgH2 on the hydrogenated microstructure of the adsorbents that were confirmed by using XPS analysis technique. SAED pattern of hydrogenated metals attributed the polycrystalline nature of mixed metals and ensured the hydrogenation to Mg2NiH4 and MgH2 compounds. Flower-like rough surface of mixed metals showed high hydrogenation capacity. The densityfunctionaltheory (DFT predicted hydrogenation properties; enthalpy and entropy changes of hydrogenated microstructure of MgH2 and Mg2NiH4 are −62.90 kJ/mol, −158 J/mol·K and −52.78 kJ/mol, −166 J/mol·K, respectively. The investigation corresponds to the hydrogen adsorption feasibility, reversible range hydrogenation thermodynamics, and hydrogen desorption energy of 54.72 kJ/mol. DFT predicted IR band for MgH2 and Mg2NiH4 attributed hydrogen saturation on metal surfaces.

We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.

We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.

The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-densityfunctionaltheory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and densityfunctionaltheory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a densityfunctional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The densityfunctional is a function of the total density and the on-top pair density rather than

We present a three-dimensional molecular densityfunctionaltheory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Among other applications, complex absorbing potentials (CAPs) have proven to be useful tools in the theory of metastable states. They facilitate the conversion of unbound states of a finite lifetime into normalized bound states with a complex energy. Adding CAPs to a conventional Hamiltonian turns it into a non-Hermitian operator. Recently, we introduced a complex densityfunctionaltheory (CODFT) that extends the Kohn-Sham method to the realm of non-Hermitian systems. Here, we combine CAPs with CODFT and present the first application of CODFT to metastable systems. In particular, we consider the negative ions of the beryllium atom and the nitrogen molecule. Using conventional exchange-correlation functionals as functionals of a complex density, the resonance positions and the resonance lifetimes are obtained, and they are in line with the findings of other studies.

We present the first analytic implementation of cubic and quartic force constants at the level of Kohn–Sham density-functionaltheory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange–correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree–Fock results. The Hartree–Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level densityfunctionaltheory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level densityfunctionaltheory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

The reflectivity of shocked xenon was measured in the experiments of Mintsev and Zaporoghets for wavelength 1064 nm. But there is no adequate theoretical explanation of these reflectivity results in the framework of the standard methods of nonideal plasma theory. The assumption of significant width to the shock front gives a good agreement with the experimental data. However, there are no evidences of this effect in the experiment. Reflectivity of shocked compressed xenon plasma is calculated in the framework of the densityfunctionaltheory approach as in. Dependencies on the frequency of incident radiation and on the plasma density are analyzed. The Fresnel formula for the reflectivity is used. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the dielectric function. The real part of the dielectric function is calculated by means of the Kramers-Kronig transformation. The approach for the calculation of plasma frequency is developed.

In the room temperature and nitrogen conditions, we presented well-resolved absorption spectra and indexes of refraction of bactericide molecules in the far infrared radiation (FIR) spectral region recorded by terahertz time-domain spectroscopy (THz-TDS). As illustrative examples we discussed the absorption spectra of captan and folpet in THz region. The absorption coefficient and index of refraction of them were obtained. Meanwhile, densityfunctionaltheory (DFT) with software package Gaussian 03 using B3LYP theory was employed for optimization and vibration analysis. With the help of Gaussian View 3.09, the distinct absorption peaks of those molecules were assigned with reliable accuracy. They were caused by intermolecular hydrogen-bonding, molecular torsion or vibration modes, absorption of water molecules, etc. As the absorption spectra are highly sensitive to the overall structure and configuration of the molecules, the THz-TDS procedure can provide a direct fingerprint of the molecular structure or conformational state of a compound.

In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-densityfunctionaltheory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.

We present a three-dimensional molecular densityfunctionaltheory (MDFT) of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: ($i$) a scalar density and a vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and ($ii$) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

We generalize a recently developed polymer densityfunctionaltheory (PDFT) for polydisperse polymer fluids to the case of equilibrium random copolymers. We show that the generalization of the PDFT to these systems allows us to obtain a remarkable simplification compared to the monodispersed polymers. The theory is used to treat a model for protein aggregation into linear filaments in the presence of surfaces. Here we show that, for attractive surfaces, there is evidence of significant enhancement of protein aggregation. This behaviour is a consequence of a surface phase transition, which has been shown to occur with ideal equilibrium polymers in the presence of sufficiently attractive surfaces. For excluding monomers, this transition is suppressed, though an echo of the underlying ideal transition is present in the sudden change in the excess adsorption.

We extend our previous definition of the metric Δr for electronic excitations in the framework of the time-dependent densityfunctionaltheory [C. A. Guido, P. Cortona, B. Mennucci, and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)], by including a measure of the difference of electronic position variances in passing from occupied to virtual orbitals. This new definition, called Γ, permits applications in those situations where the Δr-index is not helpful: transitions in centrosymmetric systems and Rydberg excitations. The Γ-metric is then extended by using the Natural Transition Orbitals, thus providing an intuitive picture of how locally the electron density changes during the electronic transitions. Furthermore, the Γ values give insight about the functional performances in reproducing different type of transitions, and allow one to define a "confidence radius" for GGA and hybrid functionals.

The geometry, electronic structure and chemical reactivity of a pyridinium-based ionic liquid, pyridinium hydrogen sulfate ([H-Pyr]+[HSO4]-), have been discussed on the basis of quantum chemical densityfunctionaltheory calculations using B3LYP/6-311+G(d,p) and B3LYP/6-311++G(2d,2p) approaches. The calculations indicated that [H-Pyr]+[HSO4]- exists in the form of an ion pair. A large electropositive potential was found on the pyridinium ring, while the regions of a negative electrostatic potential is linked with the lone pair of electronegative oxygen atoms in hydrogen sulfate anion ([HSO4]-). Electron transfer both within the anion, and between the anion and cation of an ion pair were described using natural bond orbital theory. The energy values of -7.1375 and -2.8801 eV were related to HOMO and LUMO orbitals, respectively.

We develop a theory to describe solid-solid phase transitions. The densityfunctional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials u (r ) =ɛ "close="1 /n )">σ /r n , where parameter n measures softness of the potential. We find that for 1 /n ≥0.154 the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.

A general implementation of the lowest nonvanishing order perturbation theory for the calculation of molecular multiphoton ionization cross sections is proposed in the framework of densityfunctionaltheory. Bound and scattering wave functions are expanded in a multicentric basis set and advantage is taken of the full molecular point group symmetry, thus enabling the application of the formalism to medium-size molecules. Multiphoton ionization cross sections and angular asymmetry parameters have been calculated for the two- and four-photon ionization of the H(2) (+) molecule, for linear and circular light polarizations. Both fixed and random orientations of the target molecule have been considered. To demonstrate the efficiency of the proposed methodology, the two-photon cross section and angular asymmetry parameters for the HOMO and HOMO-1 orbital ionization of benzene are also presented.

Full Text Available Conventional frontier molecular orbital theory is not able to satisfactorily explain the regioselectivity outcome of the nitrilimine–alkene cycloaddition. We considered that conceptual densityfunctionaltheory (DFT could be an effective theoretical framework to rationalize the regioselectivity of the title reaction. Several nitrilimine–alkene cycloadditions were analyzed, for which we could find regioselectivity data in the literature. We computed DFT reactivity indices at the B3LYP/6-311G(2d,p//B3LYP/6-31G(d,p and employed the grand potential stabilization criterion to calculate the preferred regioisomer. Experimental and calculated regioselectivity agree in the vast majority of cases. It was concluded that predominance of a single regioisomer can be obtained by maximizing (i the chemical potential difference between nitrilimine and alkene and (ii the local softness difference between the reactive atomic sites within each reactant. Such maximization can be achieved by carefully selecting the substituents on both reactants.

The binding within the ethene-argon and formaldehyde-methane complexes in the ground and electronically excited states is studied with equation of motion coupled cluster theory (EOM-CCSD), second-order Møller-Plesset perturbation theory (MP2) and densityfunctionaltheory with dispersion corrections (DFT-D). Electronically excited states are studied within MP2 and Kohn-Sham DFT formalisms by exploiting a procedure called the maximum overlap method that allows convergence of the relevant self-consistent field equations to higher energy (or excited state) solutions. Potential energy curves computed using MP2 are in good agreement with the EOM-CCSD calculations for both the valence and Rydberg excited states studied. For the DFT-D approach, B3LYP-D3/aug-cc-pVTZ calculations are found to be in agreement with EOM-CCSD for the ground and valence excited states. However, for the π3s Rydberg state of ethene-argon and the n3s Rydberg state of formaldehyde-methane significant deviation is observed, and this disagreement with EOM-CCSD is present for a variety of DFT-D based approaches. Variation of the parameters within the D2 dispersion correction results in closer agreement with EOM-CCSD for the Rydberg states but demonstrates that a different parameterisation from the ground state is required for these states. This indicates that time-dependent densityfunctionaltheory calculations based upon a DFT-D reference may be satisfactory for excitations to valence states, but will potentially be inaccurate for excitations to Rydberg states, or more generally states where the nature of the electron density is significantly different from the ground state.

College, City University of New York, New York, NY 10065 ONR Absorption spectra DensityFunctionalTheory Molecular clusters Contents Introduction ...Clusters using DensityFunctionalTheory May 4, 2017 Approved for public release; distribution is unlimited. L. Huang S.g. LambrakoS Center for...reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching

Computational methods that can accurately and effectively predict all types of electronic excitations for any molecular system are missing in the toolbox of the computational chemist. Although various Kohn-Sham density-functional methods (KS-DFT) fulfill this aim in some cases, they become inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functionaltheory-MC-srDFT-as a new tool in the toolbox. While initial applications for systems with multireference character and double excitations have been promising, it is nevertheless important that the accuracy of MC-srDFT is at least comparable to the best KS-DFT methods also for organic molecules that are typically of single-reference character. In this paper we therefore systematically investigate the performance of MC-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2, NEVPT2, and the coupled cluster based CC2 and CC3.

We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) densityfunctionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn--Sham current density-functionaltheory (KS-CDFT). A unique feature of the non-perturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 a.u. ($\\sim 235000$T) in strength. CDFT functionals based on the TPSS and B98 forms are investigated and their performance is assessed by comparison with accurate CCSD(T) data. In the weak field regime magnetic properties such as magnetizabilities and NMR shielding constants show modest but systematic improvements over GGA functionals. However, in strong field regime the mGGA based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T...

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) densityfunctionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current densityfunctionaltheory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

The magnetic ground state of the series of lanthanide and actinide trivalent ions is investigated by means of spin-polarized relativistic spin-densityfunctionaltheory. In the local densityfunctional approximation (LDA) an internal effective magnetic field due to exchange and correlation couples to the spin degrees of freedom. The resulting set of coupled Dirac equations yields ground-state multiplets that obey the well-known Hund's rules. This remarkable result comes about by the coupling of the j = l + 1/2 with the j = l - 1/2 states due to the exchange - correlation potential that is, as usual, the functional derivative of the exchange - correlation energy with respect to the spin magnetic moment. The effect of the coupling is shown to depend on the varying relative strengths of spin - orbit coupling and exchange splitting within the f series. Since in the f levels the internal exchange splitting dominates rather than the spin - orbit splitting, the energy level scheme is that of the Paschen - Back effect, and thus features of the Russell - Saunders coupling persist in spite of relativistic effects.

Infrared spectroscopy is an important source of information for the identification of the compounds structure and it is great significant for biological activity research of natural and organic drug molecules. With the theoretical calculation method is more reasonable and calculation accuracy continues to improve, Theoretical calculate advantage is more obvious in the infrared spectrum simulation and vibration modes attributable identified. And it has important reference value for experimental study of infrared spectral analysis. Using densityfunctionaltheory, geometry optimizations and frequencies calculation of 7-Hydroxycoumarin were performed at the level of B3LYP/6-311G(d, p), the stable structure and all vibration modes of 7-Hydroxycoumarin were attained. The results show that the infrared absorption peak of 7-hydroxycoumarin is mainly distributed in the several regions in wave number of 3 700-3 500, 3 150-3 000, 1 750-1 400, 1 400-1 000, 1 000-50 cm(-1). In addition to the vibration in a wave number range of 3 700-3 500, 3 150-3 000 cm(-1) is relatively independent, and were attributed to OH stretching vibration and benzene ring CH stretching vibration, the other several vibration regions are more complex, the different degree of spectral peaks is composed of multiple vibration modes. Finally, based on the theoretical analysis of the vibration mode, the vibration modes of 7-Hydroxycoumarin molecule were assigned, and in order to discuss the reliability of theoretical calculation method, the correlation diagram of the main absorption peak of 7-hydroxyl group was drawn from the theoretical value of X axis and the experimental value of Y axis, the correlation between experimental IR data and calculated IR data of 7-Hydroxycoumarin was analyzed through the linear regression method. Results show that they have good correlation, correlation coefficient values "r" equals 0.998 5, and the theory calculation of 7-Hydroxycoumarin IR by densityfunctionaltheory at

Classical density-functionaltheory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functionaltheory to multi-site molecular fluids has so far been limited by complications due to the implicit molecular geometry constraints on the site densities, whose resolution typically requires expensive Monte Carlo methods. Here, we present a general scheme of circumventing this so-called inversion problem: compressed representations of the orientation density. This approach allows us to combine the superior iterative convergence properties of multipole representations of the fluid configuration with the improved accuracy of site-densityfunctionals. Next, from a computational perspective, we show how to extend the DFT++ algebraic formulation of electronic density-functionaltheory to the classical fluid case and present a basis-independent discretization of our formulation for molecular classical de...

A finite temperature version of 'exact-exchange' densityfunctionaltheory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.

The calculation of atomization energies using densityfunctionaltheory (DFT), using the B3LYP hybrid functional, is reported. The sensitivity of the atomization energy to basis set is studied and compared with the coupled cluster singles and doubles approach with a perturbational estimate of the triples (CCSD(T)). Merging the B3LYP results with the G2(MP2) approach is also considered. It is found that replacing the geometry optimization and calculation of the zero-point energy by the analogous quantities computed using the B3LYP approach reduces the maximum error in the G2(MP2) approach. In addition to the 55 G2 atomization energies, some results for transition metal containing systems will also be presented.

The electronic structure and size-scaling of optoelectronic properties in cycloparaphenylene carbon nanorings are investigated using time-dependent densityfunctionaltheory (TDDFT). The TDDFT calculations on these molecular nanostructures indicate that the lowest excitation energy surprisingly becomes larger as the carbon nanoring size is increased, in contradiction with typical quantum confinement effects. In order to understand their unusual electronic properties, I performed an extensive investigation of excitonic effects by analyzing electron-hole transition density matrices and exciton binding energies as a function of size in these nanoring systems. The transition density matrices allow a global view of electronic coherence during an electronic excitation, and the exciton binding energies give a quantitative measure of electron-hole interaction energies in the nanorings. Based on overall trends in exciton binding energies and their spatial delocalization, I find that excitonic effects play a vital role...

Pressure-dependent mechanical, vibrational and Raman spectroscopic study of the cubic boron nitride in context of recent experimental Raman spectroscopic has been performed using the ab initio calculations based on densityfunctionaltheory. Detailed analysis of the pressure-dependent mechanical and phonon properties shows that the pressure significantly affects the elastic constants and phonon frequencies. There is a systematic variation of elastic properties with pressure while a polynomial expression is used to fit the pressure dependence of the Raman shift. The longitudinal optical-transverse optical (LO-TO) splitting reduces with pressure, and the intensity of both LO and TO peaks start diminishing after 750 GPa. The phonon dispersion curves up to 1000 GPa indicate its dynamical stability. The lower slope of frequency versus pressure for the LO and TO modes at higher pressures suggests its use for pressure calibration at higher pressures.

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio timedependent densityfunctionaltheory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases,the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction (blueshifts). In addition,the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics,different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing,optical spectroscopy,and so on.

A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining densityfunctionaltheory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on the femtosecond dynamics of the electron density in the hydrogen molecule interacting with high-intensity laser fields. For this purpose, the GNLSE is solved numerically for many time-steps over a total interaction time of 100 fs, by employing a finite-difference scheme. Various time-dependent (TD) quantities, namely, electron density, ground-state survival probability and dipole moment have been obtained for two laser wavelengths and four different intensities. The high-order harmonics generation (HHG) is also examined. The present approach goes beyond the linear response formalism and, in principle, calculates the TD electron density to all orders of change.

Electron dispersion forces play a crucial role in determining the structure and properties of biomolecules, molecular crystals, and many other systems. However, an accurate description of dispersion is highly challenging, with the most widely used electronic structure technique, densityfunctionaltheory (DFT), failing to describe them with standard approximations. Therefore, applications of DFT to systems where dispersion is important have traditionally been of questionable accuracy. However, the last decade has seen a surge of enthusiasm in the DFT community to tackle this problem and in so-doing to extend the applicability of DFT-based methods. Here we discuss, classify, and evaluate some of the promising schemes to emerge in recent years. A brief perspective on the outstanding issues that remain to be resolved and some directions for future research are also provided.

The microscopic reaction mechanism for methanol oxidation on Au(1 1 1) surface has been thoroughly investigated by means of densityfunctionaltheory (DFT) computations. The adsorption geometries and energies were obtained for all the adsorbates, including the reactants, the products, and various possible intermediates on the metal. According to different oxygen conditions, we propose two possible reaction pathways for methanol oxidation on Au(1 1 1): (1) HCHO esterification: the intermediate formaldehyde and methoxy couple to yield methyl formate at low oxygen coverage or without the presence of oxygen atoms; (2) HCHO oxidation: the formaldehyde is oxidized to form formate at high oxygen coverage, which further dissociates to give CO2. Our study emphasizes the critical role of oxygen coverage during the methanol oxidation reaction, and can perfectly explain the difference in product distributions observed in previous experiments.

By using ab initio densityfunctionaltheory the structural and electronic properties of isolated and bundled (8,0) and (6,6) silicon carbide nanotubes (SiCNTs) are investigated. Our results show that for such small diameter nanotubes the inter-tube interaction causes a very small radial deformation, while band splitting and reduction of the semiconducting energy band gap are significant. We compared the equilibrium interaction energy and inter-tube separation distance of (8,0) SiCNT bundle with (10,0) carbon nanotube (CNT) bundle where they have the same radius. We found that there is a larger inter-tube separation and weaker inter-tube interaction in the (8,0) SiCNT bundle with respect to (10,0) CNT bundle, although they have the same radius.

We present the results of ab initio densityfunctionaltheory calculations on the energetic, and geometric and electronic structure of Li-intercalated (6,6) silicon carbide nanotube (SiCNT) bundles. Our results show that intercalation of lithium leads to the significant changes in the geometrical structure. The most prominent effect of Li intercalation on the electronic band structure is a shift of the Fermi energy which occurs as a result of charge transfer from lithium to the SiCNTs. All the Li-intercalated (6,6) SiCNT bundles are predicted to be metallic representing a substantial change in electronic properties relative to the undoped bundle, which is a wide band gap semiconductor. Both inside of the nanotube and the interstitial space are susceptible for intercalation. The present calculations suggest that the SiCNT bundle is a promising candidate for the anode material in battery applications.

As Kohn-Sham densityfunctionaltheory (KSDFT) being applied to increasingly more complex materials, the periodic boundary condition associated with supercell approaches also becomes unsuitable for a number of important scenarios. Green's function embedding methods allow a more versatile treatment of complex boundary conditions, and hence provide an attractive alternative to describe complex systems that cannot be easily treated in supercell approaches. In this paper, we first revisit the literature of Green's function embedding methods from a numerical linear algebra perspective. We then propose a new Green's function embedding method called PEXSI-$\\Sigma$. The PEXSI-$\\Sigma$ method approximates the density matrix using a set of nearly optimally chosen Green's functions evaluated at complex frequencies. For each Green's function, the complex boundary conditions are described by a self energy matrix $\\Sigma$ constructed from a physical reference Green's function, which can be computed relatively easily. In th...

Full Text Available Densityfunctionaltheory studies of structural and electronic properties of small clusters were performed. For each cluster an optimization of structure and the basic properties of the band structure were conducted. It was determined that with increasing (n energetically more efficient in the small clusters is stabilization from the ring to fulleren-like structures containing tetragonal and hexagonal faces and all atoms have coordination number equal three. Among the clusters (ZnO12 with doped atoms most stable are clusters where Zn was replaced by Mn, Cu and Co atoms. Band gap in the electronic spectrum of doped clusters decreases due to p-d hybridization orbitals of the impurity atom with the orbitals of the oxygen atom.

In approximate densityfunctionaltheory (DFT), the self-interaction error is a pervasive electron delocalization associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using computationally efficient, constraint-resembling methods such as DFT + Hubbard U (DFT+U). Constrained DFT (cDFT) exactly enforces conditions on DFT by means of self-consistently optimized Lagrange multipliers, and its use to automate DFT+U type corrections is a compelling possibility. We show that constraints beyond linear order are incompatible with cDFT. For DFT+U, we overcome this by separating its Hubbard U parameters into linear and quadratic terms. For a one-electron system, the resulting generalized DFT+U method can recover the exact subspace occupancy and free-energy, but neither the exact total-energy nor the exact ionization potential, for reasonable parameters. Approximate functionals thus cannot be systematically corrected by constraining their...

We report here how the hydration of complex surfaces can be efficiently studied thanks to recent advances in classical molecular densityfunctionaltheory. This is illustrated on the example of the pyrophylite clay. After presenting the most recent advances, we show that the strength of this implicit method is that (i) it is in quantitative or semi-quantitative agreement with reference all-atoms simulations (molecular dynamics here) for both the solvation structure and energetics, and that (ii) the computational cost is two to three orders of magnitude less than in explicit methods. The method remains imperfect, in that it locally overestimates the polarization of water close to hydrophylic sites of the clay. The high numerical efficiency of the method is illustrated and exploited to carry a systematic study of the electrostatic and van der Waals components of the surface-solvant interactions within the most popular force field for clays, CLAYFF. Hydration structure and energetics are found to weakly depend u...

We have performed combined angle-resolved photoemission spectroscopy (ARPES) experiments and densityfunctionaltheory (DFT) calculations of the electronic structure of the Ir(111) surface, with the focus on the existence of energy band gaps. The investigation was motivated by the experimental results suggesting Ir(111) as an ideal support for the growth of weakly bonded graphene. Therefore, our prime interest was electronic structure around the [Formula: see text] symmetry point. In accordance with DFT calculations, ARPES has shown a wide energy band gap with the shape of a parallelogram centred around the [Formula: see text] point. Within the gap three surface states were identified; one just below the Fermi level and two spin-orbit split surface states at the bottom of the gap.

This paper carries out the densityfunctionaltheory calculations to study the adsorbate-substrate interaction between tetracene and Cu substrates (Cu (110) and Cu (100) surface). On each of the surfaces, two kinds of geometry are calculated, namely 'flat-lying' mode and 'upright standing' mode. For 'flat-lying' geometry, the molecule is found to be aligned with its longer molecular axis along close-packed direction of the substrata surfaces. For 'upright standing' geometry, the long axis of tetracene is found to be parallel to the surface normal of the substrate on Cu (110) surface. However, tetracene appears as 'tilted' mode on Cu (100) surface. Structures with 'flat-lying' mode have much larger adsorption energy and charge transfer upon adsorption than that with 'upright standing' mode, indicating the preference of 'flat-lying' geometry on both Cu (110) and Cu (100) surface.

We present a theoretical model for the description of the adsorption kinetics of globular proteins onto charged core-shell microgel particles based on Dynamic DensityFunctionalTheory (DDFT). This model builds on a previous description of protein adsorption thermodynamics [Yigit \\textit{et al}, Langmuir 28 (2012)], shown to well interpret the available calorimetric experimental data of binding isotherms. In practice, a spatially-dependent free-energy functional including the same physical interactions is built, and used to study the kinetics via a generalised diffusion equation. To test this model, we apply it to the case study of Lysozyme adsorption on PNIPAM coated nanoparticles, and show that the dynamics obtained within DDFT is consistent with that extrapolated from experiments. We also perform a systematic study of the effect of various parameters in our model, and investigate the loading dynamics as a function of proteins' valence and hydrophobic adsorption energy, as well as their concentration and th...

Time-dependent densityfunctionaltheory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we exte...

Full Text Available Raman scattering investigations based on densityfunctionaltheory (DFT calculations were performed to explore the vibrational modes of a cadmium hexathiohypodiphosphate CdPS3 single crystal. The calculations were performed to obtain the Raman spectra for the cadmium hexathiohypodiphosphate atoms to study the size dependence. Several vibrational modes indicating stretching and bending features related to Cd, S and P atoms were observed. Modifications of the frequency and intensity of different Raman modes with an increase in the number of atoms in CdPS3 were discussed in detail. Hydrogen atoms were added in order to make the closed shell configuration and saturate the CdPS3 as per the requisite for calculating the Raman spectra. This produced some additional modes of vibration related to hydrogen atoms. Band gap and formation energy were also calculated. The results generated are found to be in close agreement with the experimental values.

We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving quantum chemistry and nuclear physics problems based on DensityFunctionalTheory (DFT). Using low separation rank representations of functions and operators in conjunction with representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation, the Schrodinger equation, and the projector on the divergence free functions provide important examples with a wide range of applications in computational chemistry, nuclear physics, computational electromagnetic and fluid dynamics. We have implemented this approach along with adaptive representations of operators and functions in the multiwavelet basis and low separation rank (LSR) approximation of operators and functions. These methods have been realized and implemented in a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS)

Metal halide ammines have great potential as a future, high-density energy carrier in vehicles. So far known materials, e.g. Mg(NH3)6Cl2 and Sr(NH3)8Cl2, are not suitable for automotive, fuel cell applications, because the release of ammonia is a multi-step reaction, requiring too much heat...... to be supplied, making the total efficiency lower. Here, we apply densityfunctionaltheory (DFT) calculations to predict new mixed metal halide ammines with improved storage capacities and the ability to release the stored ammonia in one step, at temperatures suitable for system integration with polymer...... electrolyte membrane fuel cells (PEMFC). We use genetic algorithms (GAs) to search for materials containing up to three different metals (alkaline-earth, 3d and 4d) and two different halides (Cl, Br and I) – almost 27000 combinations, and have identified novel mixtures, with significantly improved storage...

The densityfunction B3LYP method has been used to optimize the geometries of the luteolin, thymine and lute- olin-thymine complexes at 6-31＋G＊ basis. The vibrational frequencies have been studied at the same level to ana- lyze these seventeen complexes, respectively. Theories of atoms in molecules （AIM） and natural bond orbital （NBO） have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of the complexes corrected by basis set superposition error are between -93.00-76.69 kJ/mol. The calculating results indicate that strong hydrogen bonding interactions have been found in the luteolin-thymine complexes.

Based on the densityfunctionaltheory and the atom-bond electronegativity equalization model (ABEEM), a method is proposed to construct the softness matrix and to obtain the electron population normal modes (PNMs) for a closed system. Using this method the information about the bond charge polarization in a molecule can be obtained easily. The test calculation shows that the PNM obtained by this method includes all the modes about the bond charge polarization explicitly. And the bond charge polarization mode characterized by the biggest eigenvalue, which is the softest one of all modes related with chemical bonds, can describe the charge polarization process in a molecule as exquisitely as the corresponding ab initio method.

DensityFunctionalTheory based on ab initio calculations was employed to investigate single and complex defects of oxygen in indium nitride and their influence on the optical properties. Different oxygen contents (x=1.38%, 4.16%, 5.55% and 11.11%) were considered in our study by using PBEsol-GGA and TB-mBJ for the treatment of exchange-correlation energy and potential. It was found that oxygen is energetically favorable to exist mainly as singly charged isolated defect. The results using TB-mBJ approximation predicts a narrowing of the VBM (valence band maximum) and CBM (conduction band minimum) as oxygen content increases. Nevertheless, the larger contribution of the Moss-Burstein effect leads to an effective band-gap increase, yielding absorption edge values larger than that of the intrinsic bulk indium nitride.

The N-doping effects on the electronic properties of Cu2O crystals are investigated using densityfunctionaltheory.The calculated results show that N-doped Cu2O with or without oxygen vacancy exhibits different modifications of electronic band structure.In N anion-doped Cu2O,some N 2p states overlap and mix with the O 2p valence band,leading to a slight narrowing of band gap compared with the undoped Cu2O.However,it is found that the coexistence of both N impurity and oxygen vacancy contributes to band gap widening which may account for the experimentally observed optical band gap widening by N doping.

The geometrical structures, stabilities, and electronic properties of GanLi (n = 1 - 13) clusters were investigated within the densityfunctionaltheory (DFT). The impurity lithium atom enhances the stability of GanLi (n = 1 - 13) clusters, especially GanLi (n = 9 - 13) compared to Gan(n = 9 - 14), that is at either apex position or side position. The dissociation energy, second-order energy differences, and the energy gaps between highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) indicate that the Ga7Li, Ga9Li, and Ga11Li clusters are more stable within the studied cluster range. Moreover, the variation of the average bond length of Ga-Li is due to the surface effect, and the binding strength increases resulting from the increase of charge amount.

A revised reaction mechanism of CF3I synthesis catalyzed by activated carbon is investigated with quantum chemistry methods using densityfunctionaltheory (DFT). The adsorption configurations of possible intermediates are carefully examined. The reaction pathway and related transition states are also analyzed. According to our calculations, first, the dehydrofluorination of CHF3 is catalyzed by -COOH groups, which possesses the highest barrier and is accordingly identified as the rate-determining step. Second, the difluorocarbene disproportionation over graphite (001) surface proceeds instead of dimerization. The next reaction steps involving the association of fluoromethine and trifluoromethyl, the fluorine abstractions between intermediates and the iodine abstractions by the desorbed CF3 and CF2CF3 from molecular iodine are also feasible over graphite (001) surfaces. It is also found that the coke deposition in experiments is due to the fluorine abstraction from fluoromethine. This revised mechanism is in agreement with available experimental data and our theoretical computations.

Quantum densityfunctionaltheory (DFT) results are reported for the building block [LaL1(NO3)]- of La complex [LaL1(NO3)]NO3·5H2O (L1 = (CH3)2CHCH2CH(NCHC4H3O)COO-). The structure was optimized and the calculation results show that the lanthanum ion is coordinated by one nitrogen atom and three oxygen atoms of L1 and two oxygen atoms of nitrate ion. The bond length of La-N is 0.2637 nm and the average length of La-O is 0.2526 nm, which are consistent with the literatures. In addition, the stabilities, electronic structural characteristics and IR spectra of the complex have been analyzed, which describe the coordination of lanthanum ion with other atoms in detail.

In the pursuit of enhancing the electronic properties of transparent p-type semiconductors, this work uses densityfunctionaltheory to study the effects of doping tin monoxide with nitrogen, antimony, yttrium and lanthanum. An overview of the theoretical concepts and a detailed description of the methods employed are given, including a discussion about the correction scheme for charged defects proposed by Freysoldt and others [Freysoldt 2009]. Analysis of the formation energies of the defects points out that nitrogen substitutes an oxygen atom and does not provide charge carriers. On the other hand, antimony, yttrium, and lanthanum substitute a tin atom and donate n-type carriers. Study of the band structure and density of states indicates that yttrium and lanthanum improves the hole mobility. Present results are in good agreement with available experimental works and help to improve the understanding on how to engineer transparent p-type materials with higher hole mobilities.

Structures and electronic states of graphene flakes (finite and small sized graphenes) have been investigated by means of the densityfunctionaltheory method. Sizes of graphene flakes examined in this study were n = 7, 10, 14, 19, 29 and 44, where n is the number of benzene rings in the graphene flake. The excitation energies of graphene flakes decreased gradually as a function of the number of the ring (n). The orbitals of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) are localized in the edge region of the graphene flake. It was found that the edge region can react with a water molecule and H{sub 2}O is dissociated into OH radical and hydrogen atom (H) without an activation barrier. A lithium ion can bind strongly to the edge region. The ability of the edge region in the graphene flakes was discussed on the basis of theoretical results.

An account of the performance of a modern and efficient approach to DensityFunctionalTheory (DFT) for the prediction of the photophysical behavior of a series of Ru(II) and Os(II) complexes is given. The time-dependent-DFT method was used to interpret their electronic spectra. Two different types of compounds have been analyzed: (1) a complex undergoing a light induced isomerization of one of its coordination bonds; (2) an inorganic dyads expected to undergo intramolecular photoinduced electron transfer to form a charge separated (CS) sate. Besides the noticeable quantitative agreement between computed and experimental absorption spectra, our results allow to clarify, by first principles, both the nature of the excited states and the photochemical behavior of these complex systems, thus underlying the predictive character of the theoretical approach. (authors)

All methionine aminopeptidases exhibit the same conserved metal binding site. The structure of this site with either Co2+ ions or Zn2+ ions was investigated using densityfunctionaltheory. The calculations showed that the structure of the site was not influenced by the identity of the metal ions...... oxygen, which is part of either a water molecule or a hydroxide ion. Within the site of hMetAP-2 the results strongly indicate that a hydroxide ion bridges the metal ions. By contrast, the nature of the oxygen bridging the metal ions within the metal binding site of eMetAP-1 cannot be determined based...... on the results here, due to the similar structural results obtained with a bridging water molecule and a bridging hydroxide ion....

We have thoroughly investigated the first, second and third polarizability characteristics of four hybrid chromophores by spectroscopic and computational methods. B3LYP, CAMB3LYP and BHandHLYP functionals in combination with 6-311+G(d,p) basis set were used to evaluate the polarizability and hyperpolarizability characteristics of these chromophores. Generalized Mulliken Hush analysis and frontier molecular orbital electronic distribution images of chromophores obtained from Densityfunctionaltheory computation has established the charge transfer characteristics of these hybrid chromophores. On the basis of charge transfer characteristic, these red absorbing and NIR emissive chromophores possess high nonlinear optical response. Comparison of isolated units with their analogous hybrid chromophores shows that fusion ofcoumarin with BODIPY enhances the nonlinear optical response.

For ammonia synthesis catalysts a volcano-type relationship has been found experimentally. We demonstrate that by combining densityfunctionaltheory calculations with a microkinetic model the position of the maximum of the volcano curve is sensitive to the reaction conditions. The catalytic...... ammonia synthesis activity, to a first approximation, is a function only of the binding energy of nitrogen to the catalyst. Therefore, it is possible to evaluate which nitrogen binding energy is optimal under given reaction conditions. This leads to the concept of optimal catalyst curves, which illustrate...... the nitrogen binding energies of the optimal catalysts at different temperatures, pressures, and synthesis gas compositions. Using this concept together with the ability to prepare catalysts with desired binding energies it is possible to optimize the ammonia process. In this way a link between first...

The cohesive energy, equilibrium lattice constant, and bulk modulus of noble metals are computed by different van der Waals-corrected DensityFunctionalTheory methods, including vdW-DF, vdW-DF2, vdW-DF-cx, rVV10 and PBE-D. Two specifically-designed methods are also developed in order to effectively include dynamical screening effects: the DFT/vdW-WF2p method, based on the generation of Maximally Localized Wannier Functions, and the RPAp scheme (in two variants), based on a single-oscillator model of the localized electron response. Comparison with results obtained without explicit inclusion of van der Waals effects, such as with the LDA, PBE, PBEsol, or the hybrid PBE0 functional, elucidates the importance of a suitable description of screened van der Waals interactions even in the case of strong metal bonding. Many-body effects are also quantitatively evaluated within the RPAp approach.

We formulate an ab initio downfolding scheme for electron-phonon-coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the densityfunctional-perturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.

Recently, exchange-correlation potentials in densityfunctionaltheory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke-Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke-Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.

Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant densityfunctionaltheory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration and rotational frequency dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid body value. On the contrary, superdeformed and hyperdeformed nuclei have ...

Dispersion Corrected DensityFunctionalTheory (DFT+vdW) calculations are performed to predict vibrational and thermal properties of the bulk energetic materials (EMs) β-octahydrocyclotetramethylene-tetranitramine (β-HMX) and triaminotrinitrobenzene (TATB). DFT+vdW calculations of pressure-dependent crystal structure and the hydrostatic equation of state are followed by frozen-phonon calculations of their respective vibration spectra at each pressure. These are then used under the quasi-harmonic approximation to obtain zero-point and thermal free energy contributions to the pressure, resulting in pressure-volume-temperature (PVT) EOS for each material that are in excellent agreement with experiment. Heat capacities, and coefficients of thermal expansion as functions of temperature are also calculated and compared with experiment.

We explore effects of orbital relaxation on Kohn–Sham frontier orbital energies in densityfunctionaltheory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn–Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn–Sham frontier orbital energies by Hartree–Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scaling correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.